Allam and many of the club's fans have been at loggerheads over the plans, with the Egypt-born businessman previously describing the name City as "common" and less commercially valuable.
While the Football Association membership committee have advised against the changing of the club's name, the results of this ballot could add weight to Allam's argument as they are expected to ask an FA council to go against the membership committee's recommendation.
In the vote, which saw 5,874 of 15,033 season ticket holders turn out, 2,565 fans opted for 'Yes to Hull Tigers with the Allam Family continuing to lead the club'.
Meanwhile, 2,517 said they were against the change, voting for 'No to Hull Tigers' while 792 said they were "not too concerned".
While the club explained in a statement the vote was carried out by an independent adjudication company, campaign group City Till We Die (CTWD) labelled the result "largely meaningless".
In a statement on their website, CTWD said the vote simply served as a validation of Allam's ownership and that it was a "masquerade" with "yawning deficiencies".
The group ask questions of the ballot, in particular the nature of the questions relating to the club's ownership as well as the "not bothered" option.
They also described the manner in which the ballot was conducted as "haphazard", adding: "It is a matter of great regret to CTWD that Dr Allam has continued to act so disrespectfully to Hull City supporters.
"We genuinely hope that we have now reached the end of this sorry episode.
"We call for the name Hull City to be retained for good, allowing supporters to focus their minds on the tremendous feats that Steve Bruce, the coaching staff and the playing staff have achieved thanks to the unprecedented financial generosity of Dr Allam."
