You’re making it much more complicated than necessary. Please do the following.
Back up your Mac as a matter of course. To learn how to use Time Machine please read Back up your files with Time Machine on Mac.
That just goes without saying, and is not strictly related to your AOL difficulties—if you do not back up your Mac, then by definition you have no concern about permanently losing all the information on it.
Remove the AOL email account(s) and add them again, by following these instructions: Add or remove email accounts in Mail on Mac – Apple Support. Since the account(s) may already exist, follow them in reverse. In other words follow Remove an email account, and then Add an email account. Use your AOL email address and its password.
That’s all there is to it.
I just performed Step 2 and it works just fine. Two steps and you’re done. No name, no description, nothing else is required. Of course you can add those details later if you so choose, but it’s not necessary.
I always perform Step 1.