The Premier League outfit have enjoyed a largely successful spell under the stewardship of Allam, who took over in December 2010, culminating in promotion to the top flight last season.
But his idea to rebrand the club as Hull Tigers has sparked outrage among some supporters, with Allam vehemently defending the proposal.
The row has led to Bruce calling on everyone at the KC Stadium to unite as he prepares his charges for a trip to table-toppers Arsenal on Wednesday, adding that fans should accept Allam's decisions due to his positive impact on the local community.
"We can't let it be a distraction and to be fair I'm fed up talking about it already - I think that goes for most of us," Bruce commented.
"The only thing I would say in defence of the chairman is some people don't realise he's pumped millions into a hospital here for cancer research. He's also paid £600,000 to buy a scanning machine for that hospital.
"He's only got the best interests of the club at heart. I have to tell that to all the supporters.
"It's not a situation where he's come from afar just to buy a Premier League club - he's been here for 45 years.
"The amount of work he's done for the community is remarkable. I think he bought Hull City because he didn't want Hull without a football team.
"It's a shame to be talking about these things because all the good work he has done is being soured by this name change.
"But there has to be a resolution and a way forward from it because it can only escalate and get worse."
Hull travel to Arsenal in high spirits after a superb 3-1 victory over Liverpool on Sunday, and Bruce believes the unpredictability of the Premier League is the key reason for its global appeal.
He added: "The beauty of the Premier League is that nobody can predict it. You see the big teams in Spain and Germany blow away the rest of the league, but that isn't the case so far here.
"That showcases what the Premier League is and why it is watched all over the world. It's a wonderful spectacle."
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