Allam recently caused a stir when it was revealed he had dropped the 'AFC' suffix from the club's official name after 109 years and would be focusing on marketing the team as the Tigers at home and abroad, leaving many supporters unhappy.
Bruce is uncertain of the reason why and pointed to Cardiff's decision to change their colours from blue to red as a successful rebranding.
Speaking following the 2-0 Barclays Premier League loss at Chelsea, Bruce said: "I think the PR could've handled it a bit better. I am a traditionalist.
"(But) the money our guys put into Hull City, if he wants us to play in pink and wants to call us something else, then he's entitled to do it.
"I think he just wants to do away with the 'AFC'. Why, I'm not so sure, maybe it's a marketing thing in his department."
Asked whether supporters should have been consulted, Bruce added: "Of course.
"Last year Cardiff changed their colours and there was uproar. They get promoted and is there uproar now?
"You'd have to ask him the reason why. I'm a bit of a traditionalist and maybe there's a reason why.
"There's obviously a reason why, maybe he thinks Hull City Tigers is the way forward."