What is the name of the high school principal in season 2?

The high school principal in season 2 is Principal Snyder.

Principal R. Snyder takes over Sunnydale High after Principal Bob Flutie is killed during season 1. Played by Armin Shimerman, Snyder is strict, suspicious, and openly hostile toward Buffy and her friends. He treats their unusual behavior as a disciplinary problem, even though supernatural danger repeatedly surrounds the school.

Snyder’s position gives him an important role in the show’s blend of teenage drama and horror. He represents institutional authority that is more concerned with reputation and order than with understanding what students are actually facing. His hostility toward Buffy becomes especially pointed because he views her as a disruptive influence.

Snyder remains principal through later seasons, so the answer is not limited to season 2. He is commonly confused with Principal Flutie, who led the school at the beginning of the series, or Robin Wood, who becomes principal much later. Snyder’s story ends in season 3, when the Mayor kills him during his transformation into a giant snake.