If wrong, do right (doggedly) (4)

I believe the answer is:

fido

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'right doggedly' is the definition.
The definition suggests a singular noun which matches the answer.

'if wrong do' is the wordplay.
'wrong' indicates an anagram.
'if' is an anagram of 'fi'.
'fi'+'do'='FIDO'

Can you help me to learn more?

(Other definitions for fido that I've seen before include "it would disperse fog" , "Dog perhaps" , "Typical dog's name" , "Fog disperser" .)

I've seen this clue in the Evening Standard.

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