It's becoming a kind of name (6)
I believe the answer is:
proper
'it's becoming' is the definition.
(similar in meaning)
'a kind of name' is the wordplay.
I cannot really understand how this works, but
'a' could be 'per' (eg 'one a day' means 'one per day') and 'per' is located in the answer.
'of' could be 'o' and 'o' is located in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for proper that I've seen before include "Genuine; suitable" , "Fit; accurate; decent" , "Suitable or appropriate" , "Appropriate description" , "Correct; formal" .)