The first mention is of a son of Gomer:

"And the sons of Gomer; Ashkenaz, and Riphath, and Togarmah." (Genesis 10:3)

The later individualkingdom (I see now that I have earlier misspoken) referenced by this name is evident here:

"Set ye up a standard in the land, blow the trumpet among the nations, prepare the nations against her, call together against her the kingdoms of Ararat, Minni, and Ashchenaz; appoint a captain against her; cause the horses to come up as the rough caterpillers." (Jeremiah 51:27)