Thank you BD Aqua,
As I understand it, following your instructions would create a new admin account with a new (different) name, correct?
However, just before upgrading to High Sierra I created a second admin account (just for me) with 'fictional' name. Let's call my long-time admin account iHope (my 'real' name) and the new admin account iWish.
After upgrading to High Sierra I was locked out of iHope (as described earlier) so have been using the iWish account instead without problems. I imported all my iHope documents into iWish (from backup drive) and have access to all the apps. I have not opened an Apple Mail account for iWish, nor imported the Mail account from iHope's Library.
The problem is that iWish is not in my real name (which I'd imagine would be a problem, for example, for Apple Mail and other online security). Meanwhile the iHope account is useless to me as it can't be used. I'd like to change the name of my iWish account to iHope but obviously can't do that while the original iHope admin account is still around!
That's why I'm asking whether it can be deleted, and iWish renamed iHope? If so, I'd then import Mail from the Library (from backup drive) and use Apple Mail as before?
Does it make sense or do you see problems with this idea?