Parent organised engagement around name changing (11)

'changing' is the definition.
The definition and answer can be both related to change as well as being present participle verbs.
Maybe they are linked in a way I don't understand?

'parent organised engagement around name' is the wordplay.
I cannot really see how this works, but
'parent' could be 'rear' (synonyms) and 'rear' is present in the answer.
'organised' could be 'ran' (I've seen this before) and 'ran' is found in the answer.
'name' could be 'n' (common abbreviation e.g. on forms) and 'n' is present in the answer.
'engagement' could be 'gig' (gig is a kind of engagement) and 'gig' is found in the remaining letters.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?