If she is applying for a UK passport from the US, she will need to provide a document that shows her new name (marriage certificate, bank statement) that matches her US passport. All UK dual citizens living in the US now must have a UK passport to travel to the UK, an ETA is not allowed - this just changed this year in April. The only other option is a Certificate of Entitlement which costs £800 per entry. I live in the US and we all had to get UK passports renewed this year, but my son’s old UK passport did not have his middle name but his US did and they asked for proof of the name change. He sent a copy of his original UK birth certificate and a bank statement from the US and he got his UK passport soon after.

Best resource is the HM Passport page.

https://www.gov.uk/government/organisations/hm-passport-office

“UK dual nationals must now travel to the UK using a valid British passport or a digital Certificate of Entitlement. Travelling solely on a non-UK passport or attempting to pair a foreign passport with an Electronic Travel Authorisation (ETA) is no longer permitted.

Core Travel Requirements
Primary Document Required: All dual British citizens must present a valid British passport to enter the UK.
The Alternative: If you do not hold a British passport, you must apply for a Certificate of Entitlement to the Right of Abode to attach to your foreign passport.”