Top Menu - Time and notification space. We could use that space for better purposes. Whenever the user wants the label he could just swipe down from the top.
The app is for viewing and uploading short films
I would recommend not removing that notification bar. Assuming that you are talking about the very top bar on the phone's OS that has notifications, time, battery etc (in future posts, the more specific your question the better, I had some difficulties determining what you meant).
The purpose most apps leave that alone is because that information is important to the user in almost every context, related to your app or not. Really the only exception to this is viewing content, and that bar will actively get in the way.
So if your app is viewing a short film, that would be appropriate to remove that, because that bar will take away from the video itself, and distract. But when you are talking about your main app navigation and experience, I would highly recommend following standard conventions and keeping it put.
You can auto-hide the menu when the user is scrolling down and display the menu when the user is scrolling up. I wouldn't remove the menu altogether.