On his first day in office the new independent mayor of Bristol rebranded the Council House, scrapped a parking measure brought in only a few weeks ago and announced he would take his salary in the city's local currency.

George Ferguson, who beat 14 candidates to become mayor, also revealed on Monday that the hole in the city council's budget was £32m – £4m greater than he had expected. Ferguson said he would work with anybody who could come up with a clever way of finding the savings needed without harming services.

Ferguson's first decision of his three-and-a-half year tenure was to scrap the name Council House and replace it with City Hall. At his swearing-in ceremony at Temple Meads station, he said the new name showed that the building and the work that went on inside it belonged to the people of Bristol, not to the mayor or the councillors.

Ferguson, wearing his trademark bright red trousers, also revealed that he was scrapping charges for on-street parking on Sundays. He said that from next year he would look at making parts of the city traffic-free on the first Sunday of every month, as happens in Bristol's twin city, Bordeaux.

To applause, Ferguson said he wanted to move fast. He did not want to commission expensive surveys or report on initiatives. "Let's just do it and see how it turns out," he said.

Of his salary – currently £51,000, though the figure could change – Ferguson said he would take it in Bristol pounds, a currency introduced this year and proving a success.

Thanking the voters for entrusting him with the "ultimate project", Ferguson said Bristol had a minor link to London but a more important link to the rest of the world. "We are a proud provincial city," he said. "We are pretty self-contained and we are independent."

Ferguson will try to form a rainbow cabinet with councillors from the political parties he defeated in last week's elections. He said he had already had positive talks with the leaders of all four parties on the city council.

He accepted there would be tough times ahead and revealed that at his first meeting on Monday he was told the hole in the budget was up to £32m. "We've got to be really clever," he said. "I will work with anybody who can find ways to deliver the services. I come with absolutely no dogma about how we do it. What matters is that we do it."

Ferguson completed his speech by asking everyone present to join him as he took the oath made by young men of Athens when they became citizens: "I shall not leave this city any less but rather greater than I found it."