Hull City chairman Assem Allam has not won over the fans groups after threatening to quit his role if he cannot change the club's name.
The plan needs Football Association approval and Hull fans' group City Till We Die are unhappy with Allam's threat.
"We believe the FA will be unimpressed by Dr Allam's lack of respect for their authority," said a fans' statement.
"City Till We Die are disappointed that at a time when he should be making the positive case for change and showing respect for the consultation process, which is under way, instead he is issuing threats.
"We are confident that supporters of Hull City will see through these remarks."
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