Tan has given a wide-ranging interview to the BBC in which he stands by the decision to switch the club's colours from blue to red, claims former manager Malky Mackay "got lucky" in winning promotion, criticised the British press for being "a little bit racist" in their portrayal of him and claimed that only a minority of supporters oppose his ownership of the club.
Having seen Tan dispense with one tradition, the Cardiff City Supporters' Trust now wants assurances from the Malaysian businessman that he will not seek to alter the club's name. Egyptian businessman Assem Allam, who owns Hull City, wants to rename his club Hull Tigers for commercial reasons.
"We would like a firm commitment from Mr Tan that a Hull City-style change of name will not be countenanced by him at any time in the future," Trust chairman Tim Hartley said in a statement.
"Once again, Mr Tan's interview illustrates how important it is to have strong supporter involvement in football clubs, as happens at Swansea City and many other clubs across Wales and England, and in Europe in countries like Germany."
Hartley criticised the timing of Tan's interview, with the club three points adrift of safety in the fight to stay in the Barclays Premier League, and has called on him to engage with fans' groups.
Hartley said: "We are disappointed Mr Tan has raised uncertainty about the future at a time when the team is fighting to retain Premier League status.
"Mr Tan talks about wanting to unite with fans. The first thing he could do to help towards achieving that would be to meet the Trust and Cardiff City Supporters' Club as was promised in December last year.
"Putting that meeting into the distant future is not acceptable and shows disrespect to supporters.
"While fans are grateful for the significant investment into Cardiff City, we don't believe fans need to apologise for campaigning for a return to our traditional blue colours.
"We are also concerned Mr Tan has yet to decide whether to convert the debt owed to him into equity, which is what fans were promised in no uncertain terms.
"This season should have been an exciting experience for fans after an absence of more than 50 years from the top flight, but it has been soured by continuing off-the-field distractions," added Hartley.