I'm not sure that your DS name will affect your gifts.
Some people select everyone when they gift and left the gold fall where it may. I read here that when you select everyone, the server gifts your gold randomly to three of your neighbors. (I hate that, btw)
I usually gift right after reset to the three most recent gifters on my newsfeed. I think this is what most people do, which is kinda nice since you build this mutual gift thing with them.