A little name? Little name that is a girl's name (5)
I believe the answer is:
annie
'a girl's name' is the definition.
(I know that Annie is a female given name)
'a little name little name that is' is the wordplay.
'little' suggests taking the first letters.
'little' says to take the initial letters.
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
The first letter of 'name' is 'n'.
The initial letter of 'name' is 'n'.
'a'+'n'+'n'+'ie'='ANNIE'
(Other definitions for annie that I've seen before include "musical movie" , "-- Lennox, singer" , "Popular musical about girl orphan" , "Popular stage musical" , "Musical inspired by comic strip" .)