The Levite’s namelessness (at this point, anyway) invites us to see that this man’s behaviour is typical of the Levites in those days. Furthermore, it could well be that the narrator is embarrassed about the man’s identity and is trying to protect the memory of Moses, his direct ancestor (Judges 18:30).1
7 Now there was a young man of Bethlehem in Judah, of the family of Judah, who was a Levite, and he sojourned there.