A BMW is referred to as a beamer because it is slang that was developed back when BMW's only made motorcycles. However, most people don't realize that beamer is actually an incorrect term for the car, and it should instead be bimmer.
BMW got its start with motorcycles. They were big on the race track, and BMW's biggest competitor was BSA Bikes. The initials became cumbersome to say, especially since they were so close to each other, so enthusiasts of the track developed a slang for them. BMW's were referred to as beamers while the BSA's were referred to as beesers. When the first BMW cars came out, those same enthusiasts decided that the car couldn't have the same slang as the motorcycle, so the proper slang to help differentiate the car and the motorcycle was bimmer instead of beamer. However, in time, people began using beamer to reference both.