Is there a name for the player with the most number of goals in a football game?
Perhaps the "highest scorer". No?
Yes, I have to agree with asusena. American football is a strange animal. There really is no "official" term for the highest scoring player in a game, probably because football is more a team sport. For example, if a receiver catches 5 touchdown receptions, credit for those points goes to both the quarterback and the receiver in the official game record.
For a single term describing high-scoring players, "highest scorer" or "highest scoring player" could still be used without confusion, and everyone would know what you mean. If you're talking about a non-team sport, say, singles tennis, billiards, handball, etc., then the term is simply "winner" or "victor."
What about the other football, soccer?
Sorry ... I assumed incorrectly you were asking about American football. Of course, soccer is also a team sport, and except for a well placed pass or corner kick that might count as an "assist" of sorts, scores are pretty much the result of a single individual's skill and effort. But I played soccer in college, and never heard a term to describe the highest scoring player.