Snobbish name received by glove puppet (6)
I believe the answer is:
snooty
'snobbish' is the definition.
(thesaurus)
'name received by glove puppet' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'received by' means one lot of letters goes inside another.
'glove puppet' becomes 'sooty' (British TV puppet).
'n' placed inside 'sooty' is 'SNOOTY'.
(Other definitions for snooty that I've seen before include "Disdainful" , "Snobbish (colloq.)" , "stuck up" , "No toys for being this uppity" , "Arrogantly superior" .)