Allam met with Hull fans group City Till We Die on Friday night to discuss the owner's proposal to drop 'City' from the club's name and rebrand them as Hull Tigers.
The Hull City owner revealed in the summer he wanted to ditch the Hull City AFC moniker, which has stood for the last 109 years, labelling it a 'lousy identity' and indicating the 'City' suffix was 'common'.
But after meeting with fans on Friday, Allam has vowed not to be hasty over this move and would only take such a step if it proved to add revenue to the club.
"I give my word - I won't change if no benefit is proven," Allam said.
"I could have changed the name already - I could have got rid of City already, but I haven't because it isn't proven that it will have a benefit yet."
Allam added he will not change Hull's colours of gold and black, in a clear reference to Cardiff City owner Vincent Tan.
Tan changed Cardiff's colours from blue to red and the Welsh club's crest from a bluebird to a dragon before the 2012/13 season.
"I'll never touch the colours of the club," Allam said.
"That is criminal."
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