Welshman, finally losing heart, accommodated by father and daughter (6)
I believe the answer is:
dafydd
'welshman' is the definition.
(I've seen this before)
'finally losing heart accommodated by father and daughter' is the wordplay.
'losing heart' suggests removing the centre.
'accommodated by' is an insertion indicator.
'father' becomes 'dad' (informal term for father).
'and' means one lot of letters go next to another.
'daughter' becomes 'd' (genealogical abbreviation).
'finally' with its centre taken out is 'fy'.
'fy' going into 'dad' is 'dafyd'.
'dafyd'+'d'='DAFYDD'
(Other definitions for dafydd that I've seen before include "Welsh form of David" , "Welshman" .)