Clay itself is often a nickname for Clayton. If you name your kid Clay by itself, well, that's nickname-y enough.
Famous people named Clay:
Singers Clay Aiken, Clay Cook, and Clay Walker; football players Clay Matthews II (and III); baseball players Clay Buchholz and Clay Hensley; actors Clay Greenbush and Clay Clement.
The word (and name) Clay comes from the Germanic root "glei" which means "to stick together."
100+ Bite-Sized One Syllable Middle Names For Your Cool Baby Boy, Boy Names That End In “Y”, Fab Four-Letter Names For Boys, Charming C Names For Baby Boys, Earthy Elemental Names For Baby Boys, Simple One-Syllable Boy Names, Wonderful Word Names Straight From The Dictionary, Boy Names People Won’t Shorten, Short, Sweet Baby Boy Names, Down-To-Earth Nature Names,