I dont know of an easy, clean and elegant way of doing what you ask. I wonder what happens if you edit /etc/passwd with the new name, I wouldn’t dare to try. The way I’d proceed though is to start a bare repo with my dotfiles, so if anything happens, I’m back in business with minimal configuration changes.
This is a video about bare git repo: https://www.youtube.com/watch?v=tBoLDpTWVOM&t=0
Stolen from this other video: https://www.youtube.com/watch?v=ApkoY-PN0Nk&t=0
I have debian stable with xfce on a 2014 laptop. Increasing the fonts size and using KDE connect for remote on the phone to control the whole thing. Works smoothly for video and internet, just what I need.
It’s tedious when you need to run terminal commands so I have an SSH server running there too.
For gaming maybe you want to consider moonlight utility, to stream steam games from your gaming PC to your TV PC. It’s decent for most games but forget competitive shooters.