In her first acts as New York’s new governor, Ms. Hochul has sought to distance herself from her predecessor, Andrew Cuomo, who resigned under pressure.ALBANY, N.Y. — In her first days as governor of New York, Kathy C. Hochul has gone to great lengths to demonstrate that whatever kind of leadership style she might adopt, it will be far from that of her disgraced predecessor, Andrew M. Cuomo.She immediately began providing a more complete coronavirus death toll in New York, releasing figures used by the C.D.C. that put the total at roughly 55,400, which is 12,000 more than the state figures that the Cuomo administration had regularly cited.She introduced a new ethics training requirement for all state employees, and pointedly said the state’s sexual harassment training would have to be done in person — a subtle jab at Mr. Cuomo following allegations that he never completed the state-mandated training.She replaced most of Mr. Cuomo’s inner circle with top staffers of her own. She made a point of meeting with elected officials who warred with Mr. Cuomo, including Mayor Bill de Blasio, even posting a picture on Twitter showing her laughing with the mayor over pastries.In her first week in office, Ms. Hochul has moved intently to disassociate herself from Mr. Cuomo, pursuing policies and a style of governing that cast her as the revitalizing antithesis of her predecessor.She has even gone so far as to avoid his name in her 11-minute public address on Tuesday, and, in the subsequent media blitz, has made mention of Mr. Cuomo by name only three times since taking office.Ms. Hochul, the state’s first female governor, seems focused on carving out her own space as she fills out the remainder of Mr. Cuomo’s term, which expires at the end of 2022. But Ms. Hochul may also be driven by political reasons: Future opponents, including Republicans and Democratic primary challengers, are likely to portray her as an entrenched member of the Cuomo machinery and argue that voters deserve a clean break from him.But Ms. Hochul clearly intends to portray herself as the clean-break candidate.“It’s no secret that the governor and I were not close,” Ms. Hochul told NY1 on Thursday, an assertion she has made several times this week. “He had his own tight inner circle. I created my own space.”Ms. Hochul, a Democrat and former congresswoman from Buffalo who served as Mr. Cuomo’s lieutenant governor since 2015, succeeded Mr. Cuomo when he resigned following a state attorney general investigation that concluded that he sexually harassed several women.Almost immediately, Ms. Hochul promised to open a new chapter of transparency and collaboration in state government. That broad proclamation was seen as an inherent rebuke of Mr. Cuomo, who ruled Albany with a heavy hand, using the power and influence he had amassed over more than a decade.How exactly she intends to do that remains to be seen.Ms. Hochul has so far been cautious in setting expectations for the first few months of her administration. She has singled out a handful of immediate problems she can be seen as taking decisive action on during a time of crisis — such as instituting a mask mandate in schools, or helping to expedite getting stalled relief money to struggling renters, landlords and undocumented immigrants.“She’s been smart about thematically separating herself from Cuomo without having to take any big lifts,” said John Kaehny, the executive director at Reinvent Albany, a government watchdog. “They’re picking simple things that the public can understand that are pretty unassailable from the policy perspective, like the mask mandate and releasing the C.D.C. data, and that is going to get her applause.”Ms. Hochul said that she consulted with teachers, school boards, superintendents and parent-teacher associations before issuing a mask mandate for students.Sarah Blesener for The New York TimesIndeed, Ms. Hochul did not unveil a grand vision of government or sweeping policy agenda in her first address on Tuesday. Instead, she outlined a narrow, yet urgent, set of priorities she would tackle: responding to the coronavirus and its fallout, and bringing more accountability to Albany. The actions she took this week on those fronts were seen as swift, but also as not-so-subtle admonishments of Mr. Cuomo.Richard N. Gottfried, the longest-serving member of the Assembly and the chairman of its health committee, called the expanded disclosure of Covid deaths “a very refreshing change.” Mr. Gottfried said he received a call from Ms. Hochul’s office to brief him on what the governor would announce in her first address, something he said was unimaginable under Mr. Cuomo.“Maybe it was only symbolic, but symbols at this point are what we go on,” said Mr. Gottfried, a Democrat who has served under nine governors. “Getting a call like that was an unusual and welcome experience.”Despite the early symbolic and stylistic changes, Ms. Hochul still faces hurdles in ridding the State Capitol of the last vestiges of the Cuomo era.One of the main rallying cries among Republicans, and even some Democrats, has been for Ms. Hochul to dismiss Mr. Cuomo’s top health official, Dr. Howard A. Zucker, for his potential involvement in obscuring the nursing home death toll and stonewalling health data from the Legislature last year.Ms. Hochul has not said whether she would retain Dr. Zucker, saying only that she would take up to 45 days to interview Mr. Cuomo’s cabinet officials before making a determination. The decision is complicated by the thorny optics of removing a health commissioner during a pandemic and the practical concerns of finding a replacement since so many health officials have left the state Health Department in recent months.For his part, Dr. Zucker said this week that he was “thrilled” to have Ms. Hochul as governor, suggesting that he was constrained under Mr. Cuomo from publicly disclosing certain death data.“Her leadership allowing me and all of D.O.H. to get the data out is refreshing,” Dr. Zucker said on Thursday. “Her commitment, as she has said, to transparency is revitalizing.”Another holdout from the Cuomo administration is his budget director, Robert Mujica, a close ally of Mr. Cuomo’s who has helmed the state’s finances with an iron grip since 2016 and would play a crucial role as Ms. Hochul prepares to assemble her first state budget.Mr. Mujica is lauded by supporters for his experience and competence, but derided by critics for the opaque manner in which they say he has managed the state’s coffers. His influence in state government is far-reaching: He sits on more than 30 state boards, including the Metropolitan Transportation Authority.It remains unclear whether Mr. Mujica will remain in the Hochul administration, but he has worked closely with some of Ms. Hochul’s recently recruited staffers, including her transition director, Marissa Shorenstein, and her counsel, Elizabeth Fine.State Senator Jessica Ramos, a Democrat from Queens, who has met with Ms. Hochul three times since Mr. Cuomo announced his resignation, including at a private meeting Ms. Hochul held with Latino legislators on Thursday, said Ms. Hochul had a “completely different and distinct approach to government.”The outreach by Ms. Hochul, who represented a Republican-leaning district in Congress and is regarded as a Democratic centrist, was noteworthy.“That goes to show, because, ideologically, I would argue I’m actually much more closely aligned with Cuomo than Hochul,” said Ms. Ramos, a member of the party’s left wing. “Unfortunately, her predecessor had chosen to isolate himself and hardly interacted with New Yorkers, whereas Kathy Hochul clearly likes people, and wants to talk to people and walks our streets to do so.”Before Ms. Hochul ordered a universal mask mandate in schools statewide — a divisive issue that Mr. Cuomo was seen as wanting to avoid and had left up to school districts — she held an hourlong Zoom meeting to hear from teachers, school boards, superintendents and parent-teacher associations statewide.Andrew Pallotta, president of the New York State United Teachers union, who was on the call, said Ms. Hochul had “opened up lines of communication,” describing her approach as “a breath of fresh air.”“You can’t ask for more,” Mr. Pallotta said. “It wasn’t, ‘Let me get somebody to be on this call, and then they’ll get back to me and we’ll put 12 committees together.’ It wasn’t that way at all. It was, ‘Here’s the person leading the state actually listening and responding.’”That sentiment was echoed by some county executives, who often learned about Mr. Cuomo’s coronavirus directives through his televised briefings rather than directly from his office.Anthony J. Picente Jr., the executive of Oneida County, who crossed party lines to endorse Mr. Cuomo in 2014, said the consensus among his colleagues was that there would be a “better relationship, at least in terms of communication and openness.”“We carry out what the state Health Department requires and yet were never consulted, never talked to, never a part of the overall discussions and left to pick up the pieces,” he said. “I really believe that’s not going to be the case with Governor Hochul.”Taken together, Ms. Hochul’s first moves as governor could notch her short-term policy wins, earn her good will among stakeholders and differentiate her from Mr. Cuomo to voters still getting to know her, especially as she prepares to run for governor next year.But while union leaders and legislative leaders have welcomed Ms. Hochul’s self-described collaborative approach, some government watchdogs have been more skeptical, expressing cautious optimism while waiting to see just how far Ms. Hochul will go to root out graft in Albany.“It’s a good start,” Mr. Kaehny, the government watchdog director, said. “But everything she’s doing is building up for the June 2022 primary and we’re seeing things through that prism.”Republicans, including one of their leading candidates for governor, Representative Lee Zeldin, have been less forgiving. They have sought to directly link Ms. Hochul to Mr. Cuomo’s cloud of scandals, arguing that it was disingenuous of her to distance herself from him after promoting and supporting his agenda as his second in command.“Ms. Hochul needs to look as though she’s ushering in a new era in Albany, but there will be reminders all along the way that she was, at least ostensibly, Andrew Cuomo’s partner in government for going on seven years,” said William F. B. O’Reilly, a Republican political consultant in New York. “His musk won’t dissipate quickly.”The business community appears encouraged by the team Ms. Hochul has so far assembled. Karen Persichilli Keogh, her top aide, who most recently worked at JPMorgan Chase & Co., and Ms. Fine, who advised President Bill Clinton, are both seasoned political hands with experience in New York and Washington.“She has hit the ground running, acting like a governor, not a politician, which is what we need right now,” said Kathryn Wylde, president of the Partnership for New York City, an influential business lobbying group. “Yes, a clean break from Cuomo, but continuity where it is necessary for government to meet the health and economic challenges.” More