Does naruto become a sannin

No the sannin means three legendary ninja. The title was given to Jiriya Tsunadi and Orochimaru because of their legendary skills. So sannin is not a rank or organization and so naruto can't become one. Hope this helped

Um... something in your answer is kinda wrong. Naruto manages to go Sage Mode. Sage means Sannin. Look it up in NarutoPedia.