Field in site, If you place 50 ATco's in a room you will get at least 50 different answers.
It does depend on where and how you were trained.
Personally if I am sat in front of a radar I am always "radar", if I should answer the phone for the radar controller as they are busy I call myself "approach" as I would then be providing a procedural service (some of us do still hold those ratings in Nats and no I am not old)