Note on present having name (6)
I believe the answer is:
renown
'note' is the definition.
(thesaurus)
'on present having name' is the wordplay.
'on' becomes 're' ('on' can be mean 'with reference to'**).
'present' becomes 'now' (now is a kind of present).
'having' says to put letters next to each other.
'name' becomes 'n' (common abbreviation e.g. on forms).
're'+'now'+'n'='RENOWN'
(Other definitions for renown that I've seen before include "Good reputation" , "Fame and eminence" , "Plane's maximum width" , "High repute" , "High reputation, fame" .)