It’s a dog’s name? Right again! (5)
I believe the answer is:
rover
'it's a dog's name?' is the definition.
(I've seen this before)
'right again' is the wordplay.
'right' becomes 'r' (common abbreviation).
'again' becomes 'over' (as in the phrases 'start over' and 'start again').
'r'+'over'='ROVER'
(Other definitions for rover that I've seen before include "gypsy" , "Wanderer, archery mark" , "Vehicle driven remotely over extraterrestrial terrain" , "rambler" , "Nomad" .)