What is the word to describe someone whom you are a fan of?
Solution 1:
In crossword puzzles, it's usually "idol".
Various words suggest various degrees. It might be as mild as "a preference". An "object of interest" or an "object of devotion".
So it's someone you like? or someone you follow (as on Twitter)? Maybe you should just say that, instead of saying you're a "fan".
Solution 2:
If you not only admire the person but want to be like the person maybe this is appropriate:
role model NOUN A person looked to by others as an example to be imitated.