Greyhounds are a large, (tall and thin) shorthaired dog breed. They are an ancient breed and are often associated with royalty. They can be seen in Egyptian hieroglyphics as well as more (as in last several hundred years) recent oil paintings. They are thought to have been breed for their group hunting skills. They hunt by sight, rather than smell and rely on speed to run the prey down and the force of the group to complete the kill.
In more recent history greyhounds have been breed for dog racing. They are the fastest breed of dogs and can sprint at 45 miles per hour. They are useful for racing for only a short period of their relatively long life and are destroyed when their racing career is over unless rescued. This has resulted in a number of greyhound adoption programs.
Surprisingly, they make wonderful pets; even after spending their formative years in racing. Despite their speed and hunting skills they enjoy the company of people. They are what I call a "leaning dog". They crave body contact and will frequently lean against their owner. They have very little body fat and must be protected from the cold with appropriate clothing. They require less exercise than most large dogs and appear to be like a lion in this aspect. They do a sprint then rest for 2 days. Greyhounds can live happily in a smaller house/yard than most large breeds as long as they are taken out for walks and run several times a week.
Presumably, the greyhound bus company wishes to be associated with the speed, attractiveness and lofty nature of the dog breed. Good luck! I have never seen an attractive Greyhound bus station. Recently I had cause to pick up a passenger in downtown Charlottesville, VA. The station was a tiny 1 square block island of ugliness in the midst of the downtown fall beauty of the city. It was hilarious, as if a hidden line marked off lovely "Charlottesville" and over here we have the ugly "bus station".