A bit of sense, holding back my number, concealing identity (9)
I believe the answer is:
anonymous
'concealing identity' is the definition.
(an anonymous person conceals their identity)
'a bit of sense holding back my number' is the wordplay.
'bit of sense' becomes 'nous' (nous can mean common sense).
'holding' is an insertion indicator.
'back' says the letters should be written in reverse.
'number' becomes 'no.' (abbreviation).
'my'+'no'='myno'
'myno' backwards is 'onym'.
'nous' enclosing 'onym' is 'nonymous'.
'a'+'nonymous'='ANONYMOUS'
(Other definitions for anonymous that I've seen before include "Unidentified" , "Not identified by name" , "Of unknown identity" , "Having no known name" , "Unaccredited" .)