The following sentence is cited from a textbook for English learners.
Tom is a Norwich City football fan.
What does the sentence mean? Does it mean Tom comes from Norwich city or Tom is a football fan of Norwich City team?
It's true that it might mean that Tom is a football fan who comes from -- or lives in -- Norwich City, but I think most of us would understand it with your second meaning: Tom is a fan of the Norwich City football team.
Tom is a Norwich City football fan can only mean that Tom likes the Norwich team.
For the other meaning, it would be Tom is a Norwich football fan, without the word "City".
(It's possible that this could also mean that he likes the Norwich team. I am not qualified to comment on that. Perhaps someone will step in to prevent my bumbling further.(