XH558 flew for the last time in 2015 and, earlier this year, the Vulcan To The Sky Trust was forced to put the 57-year-old nuclear bomber into hibernation at its home at Doncaster Sheffield Airport.
But the trust has ambitious plans to build a new hangar which will not only provide a home for XH558 but a base for other restoration and operational aircraft projects.
Robert Pleming, who has led the project team for the last 20 years, said the Names Under XH558's Wing initiative would mark the 10th anniversary of the first post-restoration flight in October 2007, which was 14 years after its last RAF outing.
Dr Pleming said two areas of grey on XH558's wing had been allocated for the names which would only be visible close-up so they did not detract from the classic appearance of the aircraft.
He said supporters could get involved with a £30 donation.
"This opportunity to place names on the wing was not available to us before because MoD and CAA regulations on ex-military aircraft markings meant that whilst she was flying, we had to keep her external appearance in as near to original RAF markings as possible," he said.
"We are determined to celebrate the achievement, as we aim to secure not only XH558's future, but also the prospect of other heritage aviation projects.
"As well as individual supporters, we are already finding people are donating to give these as gifts, or are honouring relatives and friends in memoriam.
"This is a great way for the British public to become involved, celebrating our past, whilst helping to inspire future engineers and aviators."
XH558 lost its permit to fly at the end of October 2015 as the engineering firms who helped keep it in the air accepted they no longer had the 1950s skills available to ensure safety.
After it was grounded, 1,000 people a month visited the Vulcan at its home until February when XH558 was placed in storage because an increase in cargo traffic at the airport meant the hangar was needed for other uses.
The trust had been developing a plan for a visitor attraction around the Vulcan, including periodically opening up its powerful engines on fast taxi runs around the airport.
A month later the trust his hit a £200,000 target which meant they could keep maintaining the aircraft.
XH558 was built in 1960 and entered service with the RAF in the role of carrying Britain's nuclear deterrent to the heart of the Soviet Union.
It was the last Vulcan to fly as an RAF aircraft in 1992.
Despite being built as nuclear bombers, the Vulcans' most famous mission was in 1982 when they bombed the runway at Port Stanley during the Falklands War, a raid which has gone down in military history due to the complex multiple refuelling operation needed over such huge distances.
The opportunity to put a name on the bomber closes on October 1 ahead of a unveiling on October 18, the 10th anniversary.