Social climber’s insulting comment about name (4)
I believe the answer is:
snob
'social climber's' is the definition.
(I've seen this before)
'insulting comment about name' is the wordplay.
'insulting comment' becomes 'sob' (I can't explain this - if you can you should give a lot more credence to this answer).
'about' means one lot of letters goes inside another.
'name' becomes 'n' (common abbreviation e.g. on forms).
'sob' enclosing 'n' is 'SNOB'.
Can you help me to learn more?
(Other definitions for snob that I've seen before include "One has pretensions" , "Snooty type" , "blackleg" , "One looks down on others" , "Looker-down on others" .)