I am looking for a plugin that makes it possible that an admin that can be seen by players ingame won't have a name tag for them.

There is no name "tag" for admins, only color by default. If there is, then it must be your chat plugin.

No. What I am talking about is the name that hovers over your player model when near another player.

There is a Player.Rename method.  Never tried it, but it's there.