Hi all - I used to lurk and occasionally post in here YEARS ago, so I know this is the first place to turn to with immigration questions.

I'm currently on ILR, and have been eligible for citizenship for a number of years. The only reason I didn't apply for it after I met the requirements was that after the work permit -> unmarried partner -> ILR process, I was pretty tired of dealing with the Home Office. However, I think the time has finally come to get it sorted.
In the interim, I've gotten married. So far I've retained my own surname, but I would like to change it to match my partner's. Can someone verify that my thinking on how to go about this alongside getting my UK citizenship/passport is correct?
First step is to change my name in the UK by deed poll. As I understand it, I have to apply for citizenship with evidence of the name that the application is being made in, so the deed poll would have to come before the citizenship application. Are there any issues with a deed poll name change before being a citizen?
Once I'd changed my name by deed poll, I would go through naturalisation with the new name, including evidence of the deed poll name change in my application. UK citizenship would be issued in the new name, and I would apply for a passport using that name.
None of this would have any impact in the US, and when I file taxes, renew US passport, etc, it would all be in my original name. If I ever move back to the US I would change my name there, but for the foreseeable future there's no beneficial reason to do so that I can see.
Does all this make sense? Is there a better approach I should take?
Thanks for any advice!