What is the name of the farm where the group stays in season 2?

The group stays at Hershel's farm during much of season 2 of The Walking Dead. The property is also commonly called the Greene family farm because it belongs to Hershel Greene and his family.

Rick's group reaches the farm after Carl is accidentally shot by Otis while hunting. Otis brings Carl to Hershel, a veterinarian, whose family provides medical care and shelter. The farm becomes a temporary refuge while Rick and the others search for Carol's missing daughter, Sophia.

The apparent safety of the farm hides a serious conflict. Hershel believes the walkers in the surrounding area are sick people who may eventually be cured, so he keeps many of them—including former friends and family members—in the barn. When the barn's secret is exposed, the survivors' different beliefs about the apocalypse come into direct conflict.

The farm is eventually overrun after a large walker herd arrives, forcing both groups to flee. "Greene's farm" is a reasonable descriptive variation, but "Hershel's farm" is the familiar name used by viewers and episode summaries.