Prince Andrew faces growing calls for him to lose or relinquish his Duke of York title from those in the city.
The royal, who faces a US civil action over sexual assault allegations, returned his patronages and military titles on Thursday.
York Central MP Rachael Maskell said it was "untenable" for him "to cling on" to his duke title and his association with the city.
Prince Andrew has consistently denied the claims against him.
He stepped down from royal duties in 2019 over his friendship with convicted sex offender Jeffrey Epstein.
On Wednesday, a US court ruled that Virginia Giuffre, who claims the prince abused her in 2001, could proceed with legal action against him.
He relinquished his military titles the next day and a source told the BBC he would no longer use the style His Royal Highness in an official capacity.
Buckingham Palace made no announcement about his ducal title, prompting Labour MP Ms Maskell to air her concerns.
She tweeted: "It's untenable for the Duke of York to cling onto his title another day longer.
"This association with York must end. There's a very serious allegation made against this man of privilege and entitlement."
Prince Andrew became Duke of York, a title traditionally granted to the monarch's second son, on his marriage in 1986.
It was previously held by both the Queen's father, George VI, and her grandfather, George V.
Liberal Democrat councillor Darryl Smalley, who is the executive member for culture, leisure and communities in York, said the city's connection to the crown and the monarch was part of its history.
However, he said the prince should relinquish the title.
While the prince had the right to a presumption of innocence, the palace and the government must consider the implications of the allegations against him, Mr Smalley said.
He said he worried that "his name by association" could become a source of embarrassment for the city.
"I think many people think he has lost all his titles," he said. "In York we are acutely aware that is not the case."
However, the city's Conservative group leader Paul Doughty said he believed the tradition of innocent until proven guilty was the "cornerstone of a civilised society".
"Likewise, I also believe that someone's position, whether a royal or otherwise should have equity in law," he said.
"I therefore think it is right that the Duke is not afforded special treatment and faces the law as anyone else would."
The prince gave up a number of his patronages in both the city and the county after stepping down from royal duties in 2019.
These included his role with the York Minster Fund and the Yorkshire Air Ambulance.