Guide
This is a minor annoyance, but still one itch that occasionally needs to be scratched...
The point is that each entry in Google Authenticator should have some sort of identification, like <service name>:<associated email address, UID>, or something like that.
Or if you just happened to misspell the entry in some way.
In Google Authenticator (version 7, possibly in earlier versions as well), you can swipe the entry to the right to edit its name.
Note that the service name can't be changed, only the "code name" after the colon.
Swipe to the right on the entry to delete it.
For good measure, make sure you tap the cloud icon in the upper right - it'll sync the entries to your Google account, making it a walk in the park restoring all codes to a new mobile phone or tablet.
Sources
https://android.stackexchange.com/q/180021/561506
https://www.reddit.com/r/sysadmin/comments/1gq8wiz/renaming_entries_in_latest_google_authenticator/