Samsung has played it coy so far about the name of its "next Galaxy," but senior VP Robert Yi let it slip at the tail end of its Q1 2012 earnings call today: it's the Galaxy S III.
"We are anticipating very strong demand of Galaxy S III."
Earlier on the call, an exec said that Samsung expects the phone to be the company's "most successful smartphone ever," and the device came up a number of other times during the presentation and subsequent Q&A session, but only this once was the actual name of the handset uttered by a Samsung exec — in this case in response to a question about marketing plans for the smartphone compared to the Galaxy Note. Yi said that a global launch might be a possibility for the Galaxy S III, in case you're wondering.
Having only heard the name, however, and not having seen it in print, it's hard to say what the final spelling might be. It could be Galaxy S III, or Galaxy S3, or even Galaxy SIII, perhaps.