Hi Julia,
You can not delete a user. Once a user is created you can rename the user or make him/her inactive.
You don't specify what version of EPESI you are using, but in version 1.4.x the management of users and contacts is integrated.
First - create a contact. Generally you create a contact that belongs to the same company.
Second - open Login Panel and create a user. You need to have a valid e-mail address for that contact because a random password will be generated and e-mailed to this user's e-mail address.
You can specify the password manually but still the e-mail will be generated with the login address and username and password.
If you see [Contact not set] it means that you created a user without an associated contact. Just edit the contact (or create a new one) and choose that login (user [2] means user with ID 2) and assign it as the login.
Instead of deleting a user you just deactivate her/him:
green dot = user active (can login)
grey dot = user inactive (can not login)