I'm surprised by refusal to back name-giver (6)
I believe the answer is:
eponym
'name-giver' is the definition.
(the namesake of something eponymous)
'i'm surprised by refusal to back' is the wordplay.
'i'm surprised' becomes 'my' ('my' is an expression of surprise).
'by' says to put letters next to each other.
'refusal' becomes 'nope'.
'to back' is a reversal indicator.
'my'+'nope'='mynope'
'mynope' in reverse letter order is 'EPONYM'.
(Other definitions for eponym that I've seen before include "Word derived from person's name or placename" , "such as Black Beauty" , "Derby is a well-known one" , "Place-name derived from name of a person" , "Word or place name derived from person's name" .)