Yorkshire intends to maintain the temporary rebranding for a fortnight, which will coincide with the closure of Whitby's second last mutual, Nationwide, which is due to close its agency on December 31.
Yorkshire's chief executive, Iain Cornish, said the rebranding reflects the mutual's determination to continue to serve the people of Whitby.
"This is the first time we've become the last building society in town," he said. "But I think there will be other towns where branch closures mean we will be the last mutual left. However, I would have thought they would be smaller towns than Whitby."
A spokesman for Nationwide confirmed that the Whitby agency will close on Friday.
Nationwide, the UK's biggest building society, has been forced to cut branches following a slide in profits.
Mr Cornish said Yorkshire's rebranding underlined the fact that the society's branches were at the heart of the organisation.
"When your staff are your best asset, it makes absolute sense to have branches at the heart of your business – which is exactly what we've done at Yorkshire. In contrast to many financial providers, not only have the last 12 months seen us keep all our branches open, we've actually opened 14 more high street offices."
Yorkshire, the UK's second biggest building society, has increased its branch numbers by 34 per cent since 1997, during which time banks have shut 20 per cent of their branches and the Post Office has closed 25 per cent, according to statistics from the British Banking Association.
"It may seem like we're swimming against the tide, but our success shows we've got it right - which is why I'm happy to pledge that Yorkshire will remain Whitby's Building Society," said Mr Cornish. "Following our merger with Barnsley Building Society two years ago we committed to retain all their branches and we have also retained all the Chelsea branches."
Yorkshire's long term ambition is for everyone in the country to be within striking distance of one of its branches, which would mean the society opening another 70 to 120 branches.
"It currently has 178 branches and believes that 250 to 300 branches would give it national coverage.
"Many of our customers say they mistrust the banks and think building societies are a safer place for their money," said Mr Cornish. "So we expect a lot of people will choose to move their savings to us instead of making the 40 mile round trip to Nationwide's nearest branch in Scarborough."
Yorkshire said it has seen a very positive reaction from Whitby's residents.
"People are coming into our Whitby branch and registering which local charity they want us to support," said Mr Cornish. "We've more than doubled our business at the branch over the past three to four weeks."
One former Nationwide customer, Karen Parkes, who lives in Whitby, said she and the rest of her family have now switched to Yorkshire.
"As a busy parent I would not always have the time to make a trip to the nearest Nationwide and having the Yorkshire on the doorstep is of huge benefit to me and my family," she said.
"To me this local commitment and investment is important. We are delighted that the Yorkshire has reaffirmed its commitment to Whitby."
In addition Mrs Parkes and her family have now moved their ISA account and the children's savings to Yorkshire.
"As an investor it is important for me that my savings remain with a building society," she said. "Having dealt with other high-street banks I was really surprised at how swift and easy the transfer was."
Society with two million members
Yorkshire Building Society is the second largest building society in the UK and incorporates the Chelsea Building Society and Barnsley Building Society brands.
It has two million members, 178 branches and 84 agencies across the UK.
It says it is committed to remaining an independent mutual and return financial benefits to its members.
Yorkshire has assets of over 30bn. Currently, it costs 56p per 100 of assets in order to run the society, one of the lowest management expense ratios in the building society sector.