Requirement originally named by daughter (4)
I believe the answer is:
need
'requirement' is the definition.
('need' can be a synonym of 'requirement')
'originally named by daughter' is the wordplay.
'originally named' becomes 'nee' (I've seen this before).
'by' says to put letters next to each other.
'daughter' becomes 'd'.
'nee'+'d'='NEED'
(Other definitions for need that I've seen before include "privation" , "''A friend in .... is a friend indeed''" , "What's lacking" , "Necessity" , "Distressful situation" .)