Green’s Dictionary of Slang

(US) an insignificant person; one who has no public ‘name’, thus adj. undistinguished, unrecognised.

1993		S. King Dolores Claiborne 281: I’d dish out a few names of my own startin with ‘yellowbelly’ n ‘dirty no-name sneak’.
2000		M. Hamid Moth Smoke 185: A school that’s difficult to get into. The sort of school unlikely to admit a boy if he comes from a no-name middle-class background.
2005		J. Stahl I, Fatty 264: The no-names who walked through the door behind [‘the biggos’].