Ok like other words you learned as a child it should be broken down phonetically.
Drag-in (or more simply Dragon) and Al-lee. Dragon Ally. So why would someone who's name is anything but Ally and definately not Dragon choose such a screenname? Well that too requires a little breakdown.
Dragons are symbols usually of strength. I was once told they were symbols of inner strength and this stuck with me. As a kid I was often picked on and felt emotionally and socially weak. I adopted the symbol of dragons to hopefully bring some of that strength to myself and my persona. It helped.
Now as an "adult" (I refuse to believe in adulthood btw ;) I am not as easily hurt by the stupidity of others. But I keep the Dragon with me.
The Ally is actually the easier part to explain. My name IS Ally. But before you get all mad at me and say I lied to on twitter and facebook and you thought my name was Dana, my middle name is Allyn. Drop the N and you have Ally..... And that's what's in a name. ;-)