You can try manually removing the account. To do this, get the account's short name and then run the following command in the Terminal:
sudo dscl . delete /Users/USERNAME
When this is done, you should be able to remove the user's account directory from the /Users folder at the root of the hard drive.
Your account usernames should be unique. Open the Users & Groups system preferences and click the lock to unlock it. Then right-click your user account and show the Advanced information on it. In here check the account short name and the name of the home folder. These are the account names not to delete.
Check the same for the account you are trying to delete. Are they at all the same?
Thanks again Topher,
The account usernames are unique. Let me try to clarify with correct terms:
Old account (the one I want to keep), Name: XX, short name: YY
New account (the one I want to delete), Name: ZZ, short name: XX
If I now delete manually as follows: sudo dscl . delete /Users/XX
is the New account deleted or the Old account? Or can my mac even get confused?
In Finder, I can't see a home drive XX, only home drive YY.
Does this make sense?