When requesting an Authy phone number change, you may receive a "Merge Accounts" email if your new number is already registered under a different email address:
 

If the New phone number listed in the email is correct and belongs to you, click Continue to go forward with the account merge. You can then log into the Authy app with your new phone number, and then update the email address to the one you want to use.

If the New phone number listed in the email is not correct, please contact our Support team.