Naming/Re-Branding

Robert,

I suspect that if there is such documentation, it is closely guarded by the companies, teams, or individuals that publish their own branded distros.

(I'm sure you've seen this question on AskUbuntu already: https://askubuntu.com/questions/194062/how-can-i-replace-ubuntu-branding-with-my-own)

On my system, there are 9540 references to the word "Ubuntu"
    $ sudo grep -ir --exclude-dir="/home" Ubuntu | wc -l

In creating a custom distro, you probably want to start with:
1. Plymouth Theme
2. Grub Menu
3. Gnome Shell Theme (the top bar, side dock, GDM login screen).
4. Desktop Theme (generally window decorations per user)

You can search how to update these individually, and you would make good progress in distinguishing your distro's "Look and Feel".

Gnome has made it unnecessarily difficult to update the Shell Theme (#3) by packaging it into a resources file (/usr/share/gnome-shell/theme/Yaru/gnome-shell-theme.gresource), but it can be done.

However, completely removing ~all~ references to "Ubuntu" may be a lot more challenging.
Even Pop!_OS has references to Ubuntu all over the place.

Instead of a comprehensive step-by-step, "how to create my own distro" instructions, decide what you want to change, and search for instructions on how to do those specific pieces. You won't completely remove all references to "Ubuntu" but you should get close to what Pop~_OS, Elementary, and others have achieved.