Why are the police at Scotland Yard called bobbies?

Answer 1

These names refer to Sir Robert Peel who created the Metropolitan Police in London.
They are called bobbies after Robert Peel, who was the UK prime minister who helped create the concept of the modern police force.

London's reorganized police force went on duty on September 29, 1829. British Home Secretary Sir Robert Peel introduced the legislation establishing the new police force, hence the popular nickname for London police, "bobbies." Early London police were also called "Peelers," also for Sir Robert. His Peelian Principles called for the accountability of each officer (all officers were given individual badge numbers) and for a focus on ethical standards in crime-fighting. Peel was quoted as saying, "The police are the public and the public are the police."

Scotland Yard got its name from the street where the police headquarters were located. It purportedly had been the site of a palace used to house visiting Scottish kings in the 12th century.

Answer 2

The London Police force was the idea of Sir Robert Peel, Bobby is a shortened form of Robert, so they police were Bobbie's men.