The Malaysian billionaire has already made the controversial decision to change the club's colours from blue to red and has also installed a new crest.
And, with Cardiff eight points clear at the top of the Championship, it has been suggested that promotion to the top flight might spark further rebranding.
Asked in a BBC programme whether a name change to Cardiff Dragons was possible, Tan said: "When we know the final result of this season, then we will think what's the best way to brand it.
"When we get there we'll make a decision and, when we make a decision, we will convey it to everyone."
However, the prospect of a possible name change caused anger among Cardiff fans and Tan has now issued a statement saying it is not a possibility after all.
"I can assure all supporters that we will not be changing our name from Cardiff City Football Club, a club I am very proud to be a part of," he said.
"Our name is our identity and remains at our core. I would not want any of our supporters to be concerned that this change would be made, hoping that this personal commitment from myself removes any fears.
"I believe the colour change is positive and will bring good tidings to Cardiff City Football Club. At this point of time, no decision has been made to change the club crest for the next season.
"For the present day, all I would ask is that we all join together, continuing your excellent support at what is a critical juncture in our season.
"Our collective aim is to back (manager) Malky Mackay and his team as they work hard to bring us all success. Working together we can achieve great things in the name of Cardiff City Football Club."