changing the original admin name

on one of my sites, the admin name is admin and it is not very secure so I want to change it. So if I create a second administrator with different username, and when I demote the admin username to just contributor etc… is it ok?
Or, we must keep the original admin at all times? Is there a difference between the original admin and the new admin I create in any way, or they have exactly same full capabilities? I assume the original admin shouldnt be better than another admin just because it was first admin correct? What do you suggest me to do