Does your computer show up as a Computer as well as a Media Device?
It's showing up as a Media Device as you have media sharing switched on. I'm not a Media expert, but would imagine this is through Media Player or Windows Media Centre.
If it is showing up as a Media Centre but not as a Computer, I would imagine that you have either got Network Discovery set not to auto-discover, apart from media devices. Or, a software firewall installed that is blocking browsing computers, but allowing media sharing.