If I may say !
Fan games = Free advertising for a company ! and there is nothing better than that especially in a game made by an independant it goes directly to your brain without thinking it's an ad.
Till you don't make money and specify it's not yours and don't destroy the image of the brand /character(real fan games)
Then unless you are making a game played in top Facebook am not sure they will care about you.
The first to hear from copyright infringement will be the distribution platform ( they make money with your games through ads). If you don't make your own website and don't host it and don't put your family name on it am not sure they will spend times to look after you.
Seriously they will need to get the IP from the distribution platform and then ask the ISP ... They will just warn the distribution platform at max !
Here it's just to explain why fan games makers are not yet in jail ...