If your right leg is forward, then hold the DB in your right hand. That's what I've done in the past.
Frankly, I haven't had much success with single dumbell split squats, so I'm not sure I'd really recommend them. Even at higher reps, like 15 reps/side, I'm using 100lbs+ (and that's probably a lot less than most people use) so my grip usually fails me before I can complete the required number of reps. What can I say? I need to work on my grip strength.
In fact, since I usually do split squats and/or lunges after deadlifts, my grip is so shot that I can't even use a DB in each hand. For this reason, I stick almost exclusively to split squats/lunges with a barbell across the back.