Nick, for instance, is a man’s name (4)
I believe the answer is:
mark
This clue is a quadruple definition!!
'nick' is the first definition.
(thesaurus)
'for' acts as a link.
'instance' is the second definition.
The answer and definition can be both related to thinking as well as being singular nouns.
Maybe they are linked in a way I don't understand?
'is' acts as a link.
'a man's' is the third definition.
'name' is the fourth definition.
(I know that Mark is a name)
Can you help me to learn more?
(Other definitions for mark that I've seen before include "Point; former coin" , "Identify" , "The second Gospel" , "Smudge" , "symbol" .)