Perhaps sign one’s name on fashionable cradle in southeast (8)
I believe the answer is:
inscribe
'perhaps sign one's name' is the definition.
(to inscribe is to write on something)
'fashionable cradle in southeast' is the wordplay.
'fashionable' becomes 'in' (in can mean fashionable or trendy).
'cradle' becomes 'crib' (I've seen this before).
'in' indicates putting letters inside.
'southeast' becomes 'SE' (synonyms).
'crib' placed inside 'se' is 'scribe'.
'in'+'scribe'='INSCRIBE'
'on' is the link.
(Other definitions for inscribe that I've seen before include "Scratch" , "Write; etch" , "Engrave; dedicate" , "chase" , "Write or carve on something as a lasting record" .)