Advice needed on Naturalisation - Surname

Hello Good People,

I have a question that I'm hoping you could advice on. My Wife's (American Citizen) US passport and Indefinite leave is in her old surname (surname since birth). In the UK she uses my surname for everything (ie, bank, National insurance number etc) as our marriage certificate was only needed to do this.

Her US passport is expiring in a few months, which we obviously want to renew as well as apply for UK Naturalisation.

My questions are below:

1. Would it be best to (before applying for UK Naturalisation) - change her surname by deed poll to my surname, then apply for a BRP (as her surname would be changed to mine) and then apply for a new US passport in my surname. And then of course after apply for Naturalisation.

OR

2. Can we simply renew her US passport in her old surname, and apply for a Naturalisation in her old surname and state under section 1.6 of the Naturalisation form that she uses my surname for all purposes (bank etc) - would this be allowed?

Any advice would be greatly appreciated.

Thank you.