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.