The first user on any setup is a local user with Admin privileges. You may use the same username and password on your mini as it is only a local user. You wouldn't necessarily have "two of you showing up", but you have two accounts, each on a different machine that happen to have the same username and password.
It would be best if that first user on your Mac Mini, be something unique and specific to that machine, with a very complicated password. Then, you have a few options:
1. Enable the Open Directory in Server.app and create an account for yourself and give yourself admin privileges.
2. Create another local user for yourself and give yourself Admin privileges.
3. Just use the admin user you created for server connections.
I use option #2, and never log in using my initial Admin account unless I absolutely have to. I do everything as the 2nd Local Admin account I created for myself.
rlk