The Hull City Supporters' Trust (HCST) has again urged the club's owners to abandon plans to change the name to Hull Tigers.
Last year, the FA Council rejected owner Assem Allam's attempt to rebrand, but on Monday an arbitration tribunal ruled that the decision should be "set aside."
That was due to the involvement of Football Supporters' Federation chairman Malcolm Clarke on the sub-committee that made the initial decision.
The tribunal believed he based his decision only on what members of the City Till We Die supporters group, now part of HCST, wanted - which is for the club's 111-year-old name to remain unchanged.
It means that while the club will remain as Hull City AFC until the end of the current campaign, Allam can re-apply to change the name again ahead of the new season.
But HCST urged the club's hierarchy to abandon their lengthy campaign, believing the tribunal's decision had been based on a "very minor technicality".
"HCST urges the owners to abandon the name change application once and for all," the organisation said in a statement.
"It is clear from the evidence set out in the arbitration document that a strong and compelling case for change does not exist.
"The FA has published a 30-page arbitration document that describes why the FA Council's decision to reject the club's proposed name change has been 'set aside' on a very minor technicality, having rejected most of the arguments offered by the club.
"The Trust is disappointed with this finding -- the FA Council made a sound decision made in the interests of football in general, not just those of Hull City supporters."
The Trust said the arbitration document showed that Hull had "agreed to present a business case for the change and then failed to do so."
They added: "We believe this is because there is not and has never been any evidence that 'Hull Tigers' would generate a financial benefit."
Allam has reiterated that the club will remain for sale until he gets his name-change plans pushed through.