Take good care of your name! (6)
I believe the answer is:
handle
'take' is the definition.
(thesaurus)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for handle that I've seen before include "Manage or deal with - in manual way?" , "Feel; name (colloq.)" , "Deal with - one's name (slang)" , "Deal with; name (colloq.)" , "Manipulate; manage" .)