The ink is hardly dry on the new Google Play signage, and newly rebranded Google Play apps are already starting to drop into the
Android Market Google Play Store Android apps section. (See, isn't that easier to say?)
Google's Music, Videos and Books apps will update and rebrand themselves to Play Music, Play Movies and Play Books, if you're running Android 2.2 and above, and if you've already got them in your country of residence. (Paid apps are available in these countries, music in the U.S. only, movies in the U.S., UK, Canada and Japan, and books in the U.S., UK, Canada and Australia.)
The Android Market will update itself to the Google Play Store at some point.
More: Google Play FAQ