The first rover on Mars was named "Sojourner" and flew to Mars aboard the Mars Pathfinder mission, landing there on July 4, 1997. The rover functioned until September, when contact with Earth was lost.
No, the noun 'rover' is a common noun, a general word for anyone who spends their time wandering. A proper noun is the name of a specific person, place, or thing; for example, a Land Rover (automobile) or NASA's Mars Exploration Rover Mission.
NASA's Spirit rover landed on Mars, January 4, 2004. Its name was chosen through a NASA-sponsored student essay competition. The rover became stuck in late 2009, and its last communication with Earth was sent on March 22, 2010.