Name of chap on X (8)
I believe the answer is:
christen
'name' is the definition.
(I know that christen is a more specific form of name)
'chap on x' is the wordplay.
'chap' becomes 'chris' ().
'on' says to put letters next to each other (in a down clue, letters appear on others).
'x' becomes 'ten' (X is the Roman numeral for ten).
'chris'+'ten'='CHRISTEN'
'of' acts as a link.
(Other definitions for christen that I've seen before include "attach handle to" , "Baptize" , "Give a name to (baby)" , "Baptise and name" , "Name in church" .)