It might not really matter, but I think a console should have a pretty good name. There's something to be said about a console that has a suave, creative title.
For me, I think the console with the best name is SNK's Neo Geo.
The word 'neo' is indicative of new and different things. The Neo Geo was just that at the time of its release; new and different (perfect arcade ports in your home!). The logo is nicely drawn plus, and this is crucial, it rhymes!
The worst named console is the XBox. Anyone else think the whole 'X' thing has been done to death? 32X, Streetfighter EX, Megaman X, Revolution X, 19XX... give it a rest! Thanks Microsoft for showing us your ability to aptly name things!