Called terribly mean daughter (5)
I believe the answer is:
named
'called' is the definition.
(synonyms)
'terribly mean daughter' is the wordplay.
'terribly' is an anagram indicator.
'daughter' becomes 'd' (genealogical abbreviation).
'mean' with letters rearranged gives 'name'.
'name'+'d'='NAMED'
(Other definitions for named that I've seen before include "Designated" , "Entitled" , "Christened" , "Titled" , "Handled" .)