He wrote up his name (add initials) in loos (5)
I believe the answer is:
eliot
'he wrote' is the definition.
(I've seen this before)
'up his name add initials in loos' is the wordplay.
I cannot really see how this works, but
'name' could be 'eli' and 'eli' is present in the answer.
The remaining letters 'ot' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for eliot that I've seen before include "British poet, d. 1965" , "The Waste Land author" , "Pseudonymous writer" , "George - - (novelist)" , "One of two writers" .)