The billionaire also owns the Jacksonville Jaguars NFL franchise, but he will not be following the example of Hull City owner Assem Allam who has added Tigers to his club's name.
"We won't be becoming Fulham Jaguars," said Khan.
"I don't think they are the things [we would change]. Fulham Football Club is how it was way before my lifetime and that is hopefully how it will be a long time after I am gone.
"Both Fulham and the Jaguars really have to operate as their own entities and they have their own core fans and obviously the sports are unique.
"We want to look for areas where they can work together and I think most of those are going to be on the business side.
"Anything historical like that, I absolutely have no intention of messing with."
Khan has spoken to Al Fayed a few times since completing his takeover and plans are afoot to honour the former chairman, with the renaming of the soon-to-be-redeveloped Riverside Stand in his honour one of several ideas under consideration.
"Let's face it, I don't think the club would probably be around without Mr Al Fayed," Khan said.
"I think he is a huge part of Fulham and, with the role he played, you have to respect and honour him in some way.
"What exactly it is, there are a lot of irons in the fire but definitely I think you have to honour all his contributions towards Fulham."