Is it permissible for a famous Muslim to use their fame to advertise for a company that deals in permissible things, and does the ruling differ if the goal is only financial gain, or financial gain and fame together?

If the advertisement is for a permissible act, then there is no blame on the famous person for what he earns in return, because the basic principle in transactions is permissibility, and there is nothing to prevent taking a fee for advertising something permissible. One should be cautious about seeking fame, as it may corrupt one’s religion.