Until there's a reliable way to use the system keyboard across all platforms, I'd recommend building your own.
Here's an on-screen keyboard I made a while ago. It's hooked up to a simple word guess game, but that's just for illustration.
If you really wanted to go with the oldschool highscore name entry thing (which I don't recommend - what a pain for the player!) then I'm sure you could do that by simply cycling through a one-dimensional array that's been preloaded with the alphabet via JSON, and adding to a text object with each current position's value.