A name I had for being bashful (5)
I believe the answer is:
timid
'bashful' is the definition.
('timid' can be similar in meaning to 'bashful')
'a name i had' is the wordplay.
'a name' becomes 'tim' (**).
'i had' becomes 'id' (I'd).
'tim'+'id'='TIMID'
'for being' is the link.
(Other definitions for timid that I've seen before include "Shrinking" , "Apprehensive and unassertive" , "Fearful - shy" , "Bashful or fearful" , "Easily frightened" .)