I thought of a couple of explanations of how that lightsaber will work.

1.) Both Jedi and Sith rely on a massive amount of discipline. Some people have said that the weapon looks very inconvenient to use. Perhaps it is designed that way on purpose to make the handler a very skilled swordsman since he/she would have to be very careful with the weapon for obvious reasons. I mean, despite how much people rag on the prequels no one really complains about the double lightsaber. If anything, it's an aspect of the prequel than even people revolted by those films have at the very least passively accepted. Also, I think that the double sided saber is infinitely more dangerous to wield than this new one.

2.) It's an exhaust system/has a defensive purpose like some people have suggested in this thread. Maybe it would hurt like a bitch if you touched it, but it would be more difficult to sever a limb? Yeah, this point is weak, I know.

3.) How I'm willing to bet how it works is that as the lightsaber is in use, the "sides" will deactivate when it gets too close to the user's hand(s) and reactivate when the user's hands aren't in danger. So that way it can still serve as an extra defense in most cases. Perhaps it is mechanically or force controlled? No matter the case, I won't be surprised if the "sides" don't stay on the entire time.

Also, despite how much I put thought into it, I think it's a silly thing to get hung up on. Frankly, I just hope the film will be en enjoyable watch at the very least. A mildly silly looking lightsaber is no reason to push the panic button. I know the teaser was short, but it looks like they are only using CGI when it is only necessary, which is a big positive in my opinion.