It was unnamed in its game appearance, although it later appeared in the Archie Comics series and was given the name Silver Sonic II.
In Sonic Adventure, and it's remake Sonic Adventure DX, the robot can be spotted inside a stasis tube near Gamma's birth area in the Final Egg. Though it plays no important role in the story. It is largely unknown what happened to this robot, or what was Eggman's purposes to create it.
When Eggman went to retrieve Silver Sonic II's body and repair him, he was chased out of the city. Silver Sonic II chased Eggman all the way to the remote Prison Island, where Eggman fell down a deep hole and was presumed killed. (In fact, Eggman survived, having stumbled onto his grandfather Gerald's laboratory.)
Three months later, when Shadow the Hedgehog came to Station Square to steal the Chaos Emerald located in their bank's safe, Silver Sonic II attempted to stop him. Unfortunately, Shadow used his Chaos Control powers and destroyed the city's defender. Silver Sonic II's remains were picked up by detective J.J. Moto, and the robot has not reappeared since (it could be presumed that he is undergoing reconstruction).
The robot is, to date, the only Sonic look-a-like to appear in a game (or two if one counts the Director's cut to be a separate game) to not be fought as a boss or be a playable character (in an official Sonic game).
Since the robot went on without a name at all in it's original appearance, fans and players have called it "Mecha Sonic". However, the Archie comics later on named the robot "Silver Sonic II" which has since become it's primary name (though some still prefer to call it "Mecha Sonic").