How do I make a playerlist that doesn't replace the current one?

I also want to use a custom name that the player enters earlier on in the game. I have a string value for that name. It is located in playergui.

You probably want to use _G variables for this

To declare one, you just put _G. followed by a name

so you'd probably just need to use a table that contains all the players names, and declare it as a _G variable so you can access it from anywhere

_G.playerList = {}