Dr Allam confirmed on Thursday that he has placed Hull up for sale, having seen a proposal to rebrand the club 'Hull Tigers' rejected by the Football Association (FA) in April.
However, the Egyptian has also taken his case to the Court of Arbitration for Sport (CAS) and will remain in charge if he does get his way.
Campaign group 'City Till We Die' were set up in opposition to Allam's original proposal and lobbied the FA to turn down the idea.
And the group have once again surfaced, expressing a distaste for Dr Allam's appeal, but pleading with him to focus on the positives of his reign in Yorkshire.
A statement read: "City Till We Die (CTWD) is confident that the Football Association's decision to reject the 'Hull Tigers' name remains fair and just and that Hull City AFC can prosper under the current or new ownership.
"CTWD is disappointed to learn that chairman Dr. Allam intends to appeal to the Court Of Arbitration for Sport (CAS) over the Football Association's rejection of his plan to rename Hull City Association Football Club to 'Hull Tigers'.
"Hull City has enjoyed a period of relative stability since the FA turned down the name change application after a thorough and fair process.
"The Allam family have continued to support the club's manager Steve Bruce in the transfer market and the club has experienced a first ever FA Cup Final and a historic, but sadly short, European campaign.
"These momentous firsts, continued Premier League football, a record shirt sponsorship deal and strong season ticket sales in spite of a massive price rise have been achieved by Hull City AFC, our best ever manager Steve Bruce and owners Assem and Ehab Allam.
"CTWD continue to support the Allams' ownership of the club. We remain grateful that in 2010 they secured the future of the club when it was uncertain and we appreciate their positive contributions to the club's history in the four years since.
"However, we still see no justifiable reason to change the name of a football club that has existed and been a pillar of the local community since 1904 and we know that a significant number of the club's fans agree.
"We remain happy to work with the owners, old or new, on issues that matter deeply to fans of Hull City AFC and especially the 1,800 members of City Till We Die."
