Changing my Social Security and Passport while living in the UK

Hello! Hopefully, this fits in this category!  I was just wondering if there is a place in the UK or agency that I could get help in changing the name on my Social Security card to my married name. None of my employment in the US reflects my married name so I do not know if this is important to do or if I should just leave it ( not wanting issues for my future self!!)  Secondly have about a year left on my current passport. I will not be making any trips to the US before that and was wondering how far ahead I should update it ( I have heard six months ahead and other dates) also where is the best place to do this in the UK? I live in Edinburgh Scotland. I would be changing it to my married name as well. Thank you!

We recently applied through the Federal Benefits Unit to update our SSA record to show that we are naturalized US citizens. (This was part of our application for SS benefits)

We completed form SS-5 which I believe is the same one needed for a name change as well.  We sent the documents using Post Office special delivery, and we had our supporting documents returned within a few days.

https://www.ssa.gov/forms/ss-5.pdf