Volume_Up has a virtual keycode, and it is defined in the Windows SDK. Media_Volume_Up either does not have a virtual keycode, or it is not defined in the SDK.
If the device reports the key, button or dial as
keyboard input (not generic USB HID input), you can already send it or use it as a hotkey, and naming it is only a matter of convenience. See
the documentation for further instructions and explanation.
If I was developing a media player, I would have no idea how to allow my media player to be controlled by this key, because even now that you have told me it exists, I cannot find it in any official (Microsoft or
USB) documentation (or anywhere else, given the lack of search terms to distinguish it from the much more common Volume_Up key). I therefore doubt that it works universally. More likely, your keyboard manufacturer includes software that allows it to operate common media players.
If what you want is to control your media player's volume, you are asking for the wrong thing.