"What we can't let it do is fester because it creates, at times, when things aren't going so well, an atmosphere that none of us want," Hull manager Steve Bruce said.
"If we are Hull City Tigers or we are Hull City, whatever we are, we have got to stay together going forward because we need all the help we can get. We are a newly promoted team. We have only been three years in the Premier League in our history so we are up against it."
Bruce said he would talk with Allam.
"The chairman has put something like 70 million pounds in," Bruce said. "Without him, there wouldn't be a club or a Hull City. It would be down the tubes, in my opinion.
"However, I have got to have a conversation with him because I don't think he quite understands what it means in terms of history and tradition. All he thinks about is going forward and he thinks the brand would be better. That is his opinion but there are thousands who don't agree."
Angry Hull fans sang "We're Hull City, We'll Die When We Want" during the Liverpool game as Allam watched on from the director's box with members of his family.
Bernard Noble, the spokesman for Hull City Official Supporters Club, said the vast majority of fans want to see Allam stay as chairman but back down from his plans to press ahead with the name change.
"If the comments he made are true, they are ill-judged and they shouldn't have been said," Noble told The Associated Press. "There is a lot of anger about what he said.
"I just hope that we can draw a line under it . and concentrate on staying in the Premier League. We can revisit it at the end of the season. This is not the time for it."
Allam is not the first foreign-born owner of an English club to incur the wrath of supporters in attempts to increase the team's marketability. Cardiff, for example, has controversially changed its club crest and plays in red instead of blue at the insistence of its Malaysian owner, Vincent Tan.
But Allam's opinion is unlikely to waver. He recently said the word "City" in the name is "redundant" and "irrelevant," and that he would prove to be a trailblazer for clubs changing their names "to something more interesting."
"City, Town, County: these are meaningless," he told The Guardian newspaper in September. "In marketing, the shorter the name the more powerful think of Coca-Cola, Twitter, Apple. By next year, I will change the name to Hull Tigers."