You'll need to go into the save file and edit the name directly there if you've already set it. If you are going to do this BACKUP YOUR SAVE FOLDER as you can lose it. Just save the entire thing as a copy somewhere to be safe.
Find your save file in C:\Users\-yourname-\AppData\LocalLow\IncontinentCell\My Dystopian Robot Girlfriend\Saves and find the latest manual save that you saved. It should start with M and end in a .mdrgslot file name. Open that file in a text editor, I recommend Notepad ++, and then you'll need to find "playerName": hidden in the text.
It'll be a lot to look through but using ctrl+f might help you find it faster and if not scroll to the end as it'll be somewhere there. Then just edit the name in the "" and save the file. You don't even need to close the game, just exit to the menu, and then after changing it load the save. It should just work afterwards.
bobscrews
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I managed to figure out a way around the issue that iyfck was having, as I suffered a similar issue with the Moaning Mod. Uninstalled it and Melon while seeing if I could fix the issue.
After opening the save folder and looking through the saves in Notepad++, all the data was still there in the .mdrgslot(s), but the save.mdrg data was wiped. I then created a copy of the folder to not lose the original data and worked to fix it. I started a new game and sped through the intro, and once able to, created a new save game in slot 1. Exiting to main menu afterwards, I looked into the new M1.mdrgslot data and as expected it was overwritten to empty values expected of a new game, but crucially save.mdrg was now populated with values pointing to the M1 slot. Changing out the data saved in the M1.mdrgslot to the data that I copied from the previous M1.mdrfslot data in Notepad++ and loading the slot again properly loaded all the previous data.
It's a bit of a hassle to do, but it's definitely recoverable. No clue why the game decided to wipe save.mdrg though, might be something to do with the mod or some other thing.