I had this dilemma too (I am the UK wife, husband lives in US) and so we decided I’d just go ahead and apply for everything in my name name going forward. I got back on 14th September this year from our wedding in to UK and even with all the closures and extra bank holiday for the Queens funeral etc I had new passport, driving licence, banking, electoral register, my nursing registration, dr’s and everything else all sorted and back in my hand in my new married name as of October 4th yesterday. Those 20 days of waiting were worth it for us because now moving forward obviously everything will just be in my new married name.
I applied for a new ESTA in my married name with new passport yesterday and it was approved in 23 minutes even with putting my husband and emergency contact details. Relieved that I can visit for the next 2 years whilst the length I130 / CR1 process now commences for us.
Just coming upon one issue which is that my I94 is only showing old passport and maiden name obviously but I’ll add a note to explain that.
good luck with whatever you decide!