If I'm not mistaken, videos recorded using Apple's tools automatically hide the network name. As far as I know, it's not possible to do the same in general use without jailbreaking.
Back in the day you could connect your iPhone to your Mac and use a file browsing app to change some file. My iPhone said "DUKE" in the top left corner for a long time. I had a genius at the Apple Store actually think I jailbroke it, lol. Some genius!