A lot of place names have the name „valley“ in them, so that’s not unusual. But the only place I know of where people say they live „in The Valley“ is in the San Fernando Valley of Los Angeles, like Neal said, which incidentally is a dump. It was poorly developed in the 1950s and used to just be orange trees and orchards. Then it got bought up and developed into housing areas. Not much to get excited about.
It is surrounded North and South by smaller hills, so I suppose it really is a valley. But it is consists of multiple unincorporated areas of Los Angeles County, except for Burbank, and a few other places I suppose. Burbank is the only place I know of that got caught up in the movie /TV industry, which is what it's known for.
No, you can keep The Valley as far as I’m concerned. I guess it’s what you would call a term of art. I think it only refers to that dumpy place, with towns like Reseda, Northridge, Van Nuys, Pacoima and more. No thanks.