What is the name of the first Mars rover to successfully operate?

The first Mars rover to successfully operate was Sojourner. It reached Mars aboard NASA's Mars Pathfinder mission, which landed in Ares Vallis on July 4, 1997.

Sojourner was a small, six-wheeled rover weighing about 11.5 kilograms. It was designed as a technology demonstration to prove that a mobile robot could be deployed, commanded, and used to study rocks and soil on another planet. The rover communicated through the Pathfinder lander rather than directly with Earth.

Sojourner operated for 92 Martian sols, or about 95 Earth days, far beyond its planned mission. It examined rocks and soil with instruments including an Alpha Proton X-ray Spectrometer and helped demonstrate autonomous hazard avoidance.

A common mix-up is confusing “first rover launched” with “first rover to operate successfully.” The Soviet PrOP-M rovers were launched toward Mars in 1971 but did not complete a successful surface mission. Spirit and Opportunity arrived much later, in 2004.