Suitable name for a fine horsewoman? (8)

I believe the answer is:

arabella

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

'suitable name for a fine horsewoman?' is the definition.
I can't tell whether this defines the answer.

'name for a fine horsewoman?' is the wordplay.
'name' becomes 'Ara'.
'for' is a charade indicator (letters next to each other).
'a fine horsewoman?' becomes 'bella' (I can't justify this - if you can you should give a lot more credence to this answer).
'ara'+'bella'='ARABELLA'

Can you help me to learn more?

(Other definitions for arabella that I've seen before include "Richard Strauss opera" , "Girl" .)

I've seen this clue in the Evening Standard.

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