These are all really good questions and I can't finds an answer to any of them. If there is a method, its arcane and not widely known.
I don't know how windows works out what to call PC.
Naming Rules for Computers on a Peer-to-Peer Windows Network
Ensure your computers are named appropriately according to the following rules:
- No two computers can possess the same computer name. Ensure all computer names are unique.
- Each computer name should be no longer than 15 characters.
- Ensure no computer name contains spaces. Old versions of Windows ((Windows ME and earlier) do not recognize computers that have space characters in their names.
- Avoid special characters in computer names. Do not use any of these characters when naming Windows computers: / \ * , . " @
- Avoid using lowercase letters in a computer name whenever possible. On Windows Vista, the case of letters (upper or lower) is ignored. Older versions of Microsoft Windows, however, treat computer names as case sensitive. Entering computer names in all uppercase is recommended to avoid possible name conflicts that could prevent Windows computers from identifying each other.
https://www.lifewire.com/naming-rules-on-windows-networks-818238
Though this is fairly old based on fact the operating systems listed in quote and page only shows how to chang name in Win 7, XP or Windows 2000.
I don't know if name is listed in any file paths. If it is, I am not sure where.