In the ME3 multiplayer lobby, I've seen some people list Battlefield 3 instead as their race. How do you obtain this? Is there any other perks other than the name change?
You have to log in to Origin with an account that has an activated Battlefield 3 Online Pass, and the pack is only for the PC and Xbox 360 versions of ME3. From the Mass Effect Wiki:
Battlefield 3 Pack (Free, single-use) - Unlock your Battlefield 3 Limited Edition soldier! A kit containing items with an aesthetic inspired by Battlefield 3. Requires that the player signs in to Mass Effect 3 with an Origin account linked to a Battlefield 3 Online Pass. (PC and Xbox 360 only)