PSP next generation
I still keep playing on my PSP occasionally, physical controls are much better than screen obscuring touchscreen buttons (for most games that is). Yes the hardware may be old and the resolution low, but there are plenty of very good games. It's the perfect size for portable gaming, screen big enough not to cause eyestrain (for me).
I do have a decent Android phone, but apart from simple bird flinging or puzzle games it's not as playable. Same thing for iphone, and even more so: the screen is higher density, but smaller. My thumbs cover more of the screen. The ipad might be a nice gaming device, especially for turn based tactical games I like so much, but it's not as good for other kind of games, lacking a physical analog controls.
From what I've seen of the new device, Sony has crammed whatever control it could fit into the same form factor. The display is very good for today (as PSP was in its day, and still good enough for me), there is an extra analog nub (hooray!), touchscreen for those games that benefit from it, gyros, and the backside is a touchpad. It may turn out I don't have enough fingers for it, we'll see.
The naming? Not as elegant as "PSP" maybe, but if it's easy to pronounce it'll hold. Take Wii, for instance. What sort of a name is that? But we are all used to it, and don't bat an eyelid when we see it.