Is diet a noun

Yes, the Word diet is both a noun and a verb. For example:

Noun (the name of a person, place or thing) In the sentence below:

"I will start my diet tomorrow." The Word diet is a noun in this sentence because it is the name of a thing.

Verb (an action Word) In this sentence:

"I am going to diet until I lose 20 pounds." The Word diet is a verb because it is used as an action.