Help please: User account shows up that I didn't create

John, in either case I did not create another user with the same name.
On one machine I created a second Admin account with a different name
and on the other machine I did not. It only has Admin and Gene and
those are the two that show up during log in time but if I look under
the user folder there is Gene and Gene_2 and I cannot access Gene,
only gene_2 while logged in as Gene. I suspect something is wrong as
it's the same on both machines.

No idea what's going on with your genes However, when you are logged in as an non-admin account, you cannot access other user accounts.

Login as admin.