The Barclays Premier League club revealed on Wednesday that they had applied to the Football Association to change the playing name to Hull Tigers from next season.
But the City Till We Die group has once again stressed its opposition to Allam's plans.
In a statement released to Press Association Sport, the group said: "The City Till We Die campaign group is disappointed to learn that Hull City AFC has formally written to the Football Association requesting to change the name of our club to Hull Tigers, as of the 2014-2015 season.
"When City Till We Die met with Hull City AFC owner Dr Assem Allam on 1 November, he assured us that any name change would not occur for two to three years, and that it would not go ahead without supporter consultation, or without the benefits being proven by research. No such research or consultation has taken place.
"Commentators on the sport and experts in marketing alike have reacted to Dr Allam's name-change plans with widespread derision, while his intemperate remarks about Hull City supporters have been roundly condemned.
"Single-mindedness is not the only way to win respect; listening to the counsel of others and being prepared to concede that you may have made a mistake can also be a sign of strength. Sadly, the events of recent weeks suggest that our owner may not appreciate this.
"This matter is now in the hands of the only people who have the right to make such a decision: the football authorities."
The campaign group revealed it had supplied the FA with a timeline dossier on Allam's proposals and also met with representatives of the Premier League to voice concerns.
The statement added: "The FA is an organisation with a rich and proud history; this year, it is celebrating its 150th anniversary. This Saturday, as part of those celebrations, numerous FA dignitaries will be at the KC Stadium to honour Hull-born Ebenezer Cobb Morley, one of the founding fathers of Association Football.
"We remain confident that, with the eyes of the whole footballing world upon them, the FA will make the right decision, and act to protect not only the heritage and traditions of Hull City AFC, but also those of other clubs whose identities may come under threat in the future.
"This issue matters for all football supporters, not just the people of Hull, and the decision the FA makes will set a very important precedent.
"We urge Hull City AFC supporters who wish to keep our historic name to continue the peaceful and dignified campaigning which has brought us messages of support from all around the world, to make their voices heard by the FA both this Saturday and over the coming weeks, and to sign our petition at citytillwedie.com/petition."
Confirming the move to change the name, a Hull spokesman told Press Association Sport on Wednesday: ''We have sent a letter to the Football Association this week asking for them to consider our request to change the club's playing name from next season.''
Allam has already changed the company name to Hull City Tigers but he needs the permission of the FA Council to change the club's playing name.
Allam has offered to refund any of the club's season-ticket holders who are unhappy and has previously said he considers a Tigers brand to be more marketable, and the word ''City'' to be ''lousy'' and ''common''.
The 74-year-old Egypt-born businessman, who moved to Hull in 1968, also caused controversy earlier this month by saying of the critics: ''They can die as soon as they want, as long as they leave the club for the majority who just want to watch good football.''
Hull manager Steve Bruce believes Allam should be granted his wish.
He said last month: ''I can understand [the unhappiness] because in our country especially we are really big traditionalists and a lot of people have supported the club since the year dot, where it has been Hull City AFC.
''But the owner has come in and he's in a different culture and for the money he has put into the club if he thinks Hull Tigers is his way forward then we have to respect it.
''If he asks us to play in pink and white stripes on Saturday we have to do it because without him there wouldn't be either a Hull City or a Hull Tigers.''