What is the name for this technique to prepare eggs?
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.