It is definitely the same school it has been for quite some time. But I can understand anyone's confusion because it is located about five miles due north of New Market on 81, or about five miles due south of Mount Jackson. Yet the mailing address is Quicksburg, which is a much smaller town than either of the other two and sits to the west on or close to Rt. 42. So my guess is that some long ago post office determination made it what it is today.
When I saw your headline, I thought you would be asking about the name change to Mountain View a few years ago, only to be re-named back to Stonewall Jackson. That was a big issue about being politically correct and I guess both decisions were made by county authorities. Not sure if there was ever any public outcry one way or another.
For another example of post office puzzles, my school (Riverheads) has a Staunton mailing address, even though Staunton is 10 miles away and right off the top of my head I can think of five or six post offices that are closer to the school than Staunton.