why change your name full stop. why do we do this ?
I changed my name when I got married. Pain in the arse, thankfully I didn't not change all of my docs, so now I am changing / dropping my married name
Basically you build up a professional cv, professional brand then destroy it for what? personally, double barrel names are a bit too fussy for me and again what for? you trash your brand.

I am 48 about to start a phd. I think there are a lot of family challenges in your message. Family support does help but sometimes you just need to be a bit selfish. I think I would start by analysing very carefully what benefits you will get out of doing the phd. From an academic point of view a phd is not the same as a masters. Its a long road - more like project management and critical analysis skills it seems to me. If you are looking for motivation at this stage that is not a good place to start. You need to be super motivated. If you meant you are lacking confidence then that is something else. Lots of people lack confidence. Start perhaps by reading other phd thesis in your field you'll get a feel for what is produced at the end of a phd then ask yourself if you feel you could produce something similar with some guidance. You arent supposed to know everything at the start.