Lady I name during test on the way back (6)

'lady' is the definition.

'i name during test on the way back' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'during' indicates putting letters inside.
'test' becomes 'exam' ('exam' can be a synonym of 'test'**).
'on the way back' says the letters should be written in reverse.
'exam' backwards is 'maxe'.
'i'+'n'='in'
'in' placed into 'maxe' is 'MAXINE'.