A Parisian loved to adopt name that's plain (9)
I believe the answer is:
unadorned
'plain' is the definition.
('unadorned' can be similar in meaning to 'plain')
'a parisian loved to adopt name' is the wordplay.
'a parisian' becomes 'un'.
'loved' becomes 'adored' ('adored' can be similar in meaning to 'loved'**).
'to adopt' indicates putting letters inside.
'name' becomes 'n' (common abbreviation e.g. on forms).
'adored' placed around 'n' is 'adorned'.
'un'+'adorned'='UNADORNED'
'that's' is the link.
(Other definitions for unadorned that I've seen before include "Without embellishment" , "Not decorated, plain and simple" , "Plain, undecorated" , "Simple and plain as around den" .)