Huge name, gargantuan to some extent (4)
I believe the answer is:
mega
'huge' is the definition.
(mega can mean very large)
'name gargantuan to some extent' is the wordplay.
'to some extent' says the answer is hidden in the clue.
'MEGA' is hidden within 'name gargantuan'.
(Other definitions for mega that I've seen before include "As brilliant" , "Great American" , "wicked" , "Huge (slang)" , "Game (anag) -- great" .)