You can call the emulator whatever you want to call it in the Manage Emulators window, i'd suggest calling it Mednafen for simplicity.
You can then add multiple platforms for it like I have in the screen shot above in Associated Platforms tab. You have to have platforms added to this tab for the emulator to work in LB.
Also while we're at it, you do have Mednafen installed ? Because Mednaffe is not an emulator emulator, it is juts a GUI for Mednafen.
Here is a quick tutorial video I did for Launchbox and Retroarch, even though it is for Retroarch most of the same principles apply here except you don't need any command line parameters with Mednafen.