I've had [ So far / In Order ] -
Xbox Original
Xbox 360 Elite
Xbox 360 Shiny Slim [ I have two 360s so I can host LAN Parties. Elite downstairs, Slim upstairs in my Room.

And that is it lol
I've played on a PlayStation 1 and a PlayStation 2 at a friend's house, A little bit before I got my Xbox Original.
Before Consoles, It was all PC and DOS Games

Also, Turns out that your Xbox has actual built-in names, If you had Halo : Combat Evolved and went to the LAN Section, It would show your Xboxes' Name.
I checked all Three of my Xboxes and I got -
Xbox Original = Shadow
Xbox 360 Elite = Saucy [ lol ]
Xbox 360 Shiny Slim = Wilshire
I've heard people with Xboxes named " Donut " and " Darling ".. Even some like " Hot Dog " and " Phantom ".
If you want to check your Consoles name then I think there MIGHT be other games that show it instead of Combat Evolved.