The old user and the new user are the same thing. You just changed the name.
the old/new user was already invited and therefore you can't invite him again. You have 3 good options.
1. delete the user and create a new one (instead of just editing the old user)
2. set a password for the user and give it to the user.
3. instruct user to log in with their email address. Upon login they should click on "Forgotten Password?" which will send them an email to set themselves new password.



Reasons for choosing option 1 - you ensure that the new user actually gets a new account and doesn't get any of the personalized settings of the old user.
You prevent the new user from viewing chat messages, voicemails, meeting recordings, call recordings of the old user.