While the club's 'playing name' is still Hull City AFC, Allam changed the company name to Hull City Tigers ahead of this season.
And in the belief the adjustments will help make for a more marketable brand worldwide, he is now intending to have the playing name altered to Hull Tigers for next term, an application for which will need to be made to the Football Association by April 1.
Despite protests led by Hull fans' group City Til We Die, Allam has made clear his determination to press on with his plans.
And regarding the supporters, the Egypt-born 74-year-old told the Hull Daily Mail: "There's no need for a referendum. The crowd we get inside the stadium is the perfect referendum.
"Fans can choose to vote with their feet. If they are not happy, they can stay away.
"I am also willing to refund any unhappy season ticket holder who wants their money back.
"I understand that fans have purchased or may have purchased season tickets in the expectation they were for Hull City AFC. Having learned the AFC is now not present, they are perfectly entitled to seek a refund.
"The club will be more than happy to oblige by paying them back in full, on a pro rata basis, if they are not happy with the plans to rebrand the club."
Hull, currently 12th in the Barclays Premier League in what is their comeback top-flight season following their promotion in May, host Crystal Palace at the KC Stadium on Saturday.
The club later issued a statement elaborating on the "pro-rata" nature of the refund.
With City having already played five home games, any fan who returns their season ticket before 5pm this Friday will be refunded the cost of their season ticket less the retail price of tickets for those five games. For a full-price adult season ticket, the deduction would be £150.
Next week, following Saturday's home game against Crystal Palace, the equivalent deduction would be £172 as fans are refunded their ticket price less the retail price of the six games played.
The club statement added: "After Friday 29th November, season ticket refunds will only be offered at the club's discretion.
"Dr Assem Allam has made this offer in light of the confusion that followed the recent meeting with representatives of supporters' groups, and the fragmented messages that have emanated since that meeting.
"That meeting closed with one of the representatives requesting the opportunity to develop alternative commercial models, and nothing has yet been presented to the club.
"Dr Allam feels a sense of duty to the majority of fans and stakeholders to secure the future stability of the club, whilst continuously improving the quality of football, and as such is advancing his plans to generate the commercial opportunities necessary to forge a sustainable future.
"He is also keen that the majority of fans are able to focus on enjoying the quality of Premier League football at the KC Stadium, without being diverted on to minority interests."