Why it called the Andy Taylor show?

The show is called "The Andy Griffith Show" because the main character is Andy Taylor, the sheriff of Mayberry, North Carolina.

The show revolves around his life, his interactions with the townspeople, and his relationships with his son Opie and his deputy Barney Fife.

It's simple but effective: the show is named after the protagonist who drives the plot and whose experiences define the show's overall theme.