Lets say you are tired of the default name and want to change it.
Unfortunately, there's no way to change it in-game. Therefore, we must edit the save file.

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First, you'll need to go to where the game files are at. The easiest way to do this is through the steam launcher.
Click on the gear icon, then put your cursor on Manage, and then click on Browse local files

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Alternatively, you can right click the game on the side bar, put your cursor on Manage, and then click on Browse local files

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From there, go to your Saves folder and edit your save file in notepad (note: save files end with .celeste).
Near the top, you should find something like this:
Change whatever (your name here) is to whatever you want.

In this example, I changed it from this:
to this:

Do not forget to save changes.

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And you're done, you have successfully changed your name for that specific save file.
(go you!)

If you're using Everest, you're in luck. You can simply select the save file in-game, press rename, and go from there. This feature already comes with the mod-loader, so you don't even have to install mods for this.

This is a very useful feature if you use skin mods and don't want to see your deadname want to change the name to that of the skin that you are using.