The controversial decision, announced on Friday, will do away with the Association Football Club (AFC) moniker which has been part of the Yorkshire club's name since their formation in 1904.
Allam, who took charge of the club in 2010, told the Hull Daily Mail that he viewed the word City as "common", "irrelevant" and a "lousy identity".
He instead wants to market the club as Hull City Tigers locally and Hull Tigers to national and international audiences.
The 73-year-old millionaire's plan has been met with anger by many supporters, who feel the club's 109-year history has been disrespected.
A poll on the Facebook page of the Hull City Official Supporters' Club which asked fans if they were for, against or indifferent to the plans was overwhelmingly weighted in favour of those opposed to the idea.
Prominent Hull City blogger Rick Skelton was among those to express opposition.
He wrote: "We are not a major club in England let alone the world. That won't change with rebranding. It would only change with sustained success. So this is a pointless exercise.
"Mr Allam's assertion that the name 'Hull City' is irrelevant, that it's too common, is as disgusting a use of the English language as his new name for the club.
"It's not irrelevant, it's been the name of the club for 109 years and it matters to people.
"Those people, the fans, have fought to save Hull City numerous times down the years. It may only be a name to Mr Allam but to us, it's the name of something we love, we've cherished and will be cherished long after the current owners.
"The saddest part of all that is that this has come at a time when fans should be excited for top flight football, not angry at a ridiculous rebrand.
"And the feeling towards the Allam family - who have done wonderful things for our club and our City - should be one of fondness not fury."
Egyptian-born businessman Allam outlined his plans in an interview with the Hull Daily Mail on Friday.
"Hull City is irrelevant," said Allam, who took over the Tigers in 2010 following their relegation from the top flight and whose investment is credited with saving the club from a significant financial crisis.
"My dislike for the word 'City' is because it is common. City is also associated with Leicester, Bristol, Manchester and many other clubs. I don't like being like everyone else. I want the club to be special.
"It is about identity. City is a lousy identity. Hull City Association Football Club is so long. In Tigers, we have a really strong brand."
Any references to AFC on club branding will be phased out, although AFC will remain on the shirt crest during Hull's first season back in the Premier League, before being removed from the 2014/15 campaign.
Allam's son and vice-chairman Ehab Allam defended the decision to drop AFC from the club's name after 109 years.
"We have dropped the AFC as it is something which has become redundant," he said.
"The identity of the club is the Tigers, the stripes, and the colour scheme of amber and black, which remains."
However, Ehab Allam admitted the club could not force people to accept the rebrand.
"People have the right to call the club what they like, it's their club," he said.
The Allams' plan did, however, receive cautious support from Bernard Noble of the Hull City Official Supporters' Club.
"My personal opinion is I'm disappointed because I'm a bit of a traditionalist," he told BBC Radio 5 Live. "But this guy saved us from liquidation and administration and it's his club.
"As far as Hull City Tigers is concerned, the fans - the 25,000 people who will be there for the first home game against Norwich - they'll say 'I'm off down to watch City'.
"There will be disappointment there but I think we will realise that going into the Premier League we want to be a bit different, and he wants to be that bit different to get the business up and running.
"He's a very, very successful businessman."