PUBG in-game name updates are automatic. Once you updated your in-game name, it will be updated on Challengermode as well with a small delay.
Even if your in-game name does not match the one on Challengermode, you will still be able to play as the invitation is sent based on your unique ID.
❗️Note: If you remove your game account in order to re-add it, you won't be able to find it due to the new name not being recognized.
Running into other issues, or do you have additional questions? Feel free to chat with us by clicking (?) on Challengermode.