Write one's name on (4)
I believe the answer is:
sign
'write one's name on' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for sign that I've seen before include "Any of the 12 divisions of the Zodiac" , "Traffic control - to write one's name" , "Endorse" , "Put one's name to a document" , "Manifestation" .)