Here's how we know:
* It names a thing: Reputation refers to the general opinion people have about someone or something.
* It can be the subject of a sentence: "Her reputation as a skilled artist is well-deserved."
* It can be the object of a verb: "He built his reputation through hard work."
* It can be modified by adjectives: "A tarnished reputation"
Therefore, based on its function in a sentence and its meaning, "reputation" is classified as a noun.