What is the name for this technique to prepare eggs? I prefer to make my eggs similar sunny side up, but I flip them and cook them on both sides. I don't use oil, so they're not fried either. 

I crack them into a pre-heated pan at medium high heat, wait until the yolk solidifies a bit, and then flip them and wait a little bit less time. The yolk usually has a film over it, and often comes out somewhere between runny and solid, depending on how long I leave it.
I'd actually call those "over medium" or "over hard", not over easy. A perfect egg over easy would have all of the egg white totally cooked and solidified, but the yolk should be almost totally runny. Over medium would be a half-solid, half-runny yolk (more or less), and over hard ("over well" works too I guess, I've never heard that but maybe one of the two is a regional term) would mean the yolk is totally cooked through and solid.