A leaked section of Samsung's more recent trademark application with the USPTO, dated after the previous filing for 'GEAR', reveals that Samsung is now asking to protect the name Samsung GALAXY GEAR. The filing was made under international class 009, which is the category for wearable digital electronic devices, such as a wristwatch, and was filed on July 29th.
Considering that a smartwatch from Samsung would probably sync with its Galaxy branded handsets, adding the Galaxy name to its line of smartwatches makes a lot of sense. As we indicated earlier, Samsung is in a race with Apple to be the first to launch the new generation of smartwatches. Apple has already started applying for the iWatch trademark in various countries, but a recent report suggests that the Cupertino based company has had to hire some more engineers to get its watch to the next level in development. Based on that report, we might not see the Apple iWatch until sometime in 2014.
Thanks, Anonymous Tipster!
source: USPTO via GalaxyClub (translated)