Crossword Genius

A pettish name to call Elizabeth (5)

Ross

I believe the answer is:

libby

I'm a little stuck... Click here to teach me more about this clue!

'a pettish' is the definition.
I can't tell whether this definition defines the answer.

'name to call elizabeth' is the wordplay.
'name' becomes 'Lib'.
'to call elizabeth' becomes 'by' (I can't justify this - if you can you should believe this answer much more).
'lib'+'by'='LIBBY'

Can you help me to learn more?

(Another definition for libby that I've seen is " - - Purves, journalist and broadcaster".)

I've seen this clue in the Evening Standard.
Want a hint initially instead of a full solution? Install my app