>Does it mean that my MacBook is fake?

There's not really a market of fake MacBooks that someone can buy (outside of China and from a legit store, none the less), and think they're an Apple product. It's very hard to make a fake one to a quality that will convince anybody with any familiarity with the platform and leave enough room for profit (from materials to unibody construction, precision etc).

The @MacBook-Pro part is the name of the machine. Perhaps the name changed? Maybe you've set it to change through DHCP, whenever a new connection tries to assign one?