The name Hershey Hockey Club was an alternative official name that was used by the Hershey Bears during their early years of existance. The name was also used in that same role by the Hershey Cubs as well.
When the Bears moved to the professional level and joined the International-American Hockey League (now American Hockey League), an expansion franchise called the Hershey Cubs was established at the amateur level to replace the Bears. The Cubs joined the Eastern Amateur Hockey League, the previous league that the Bears played in. The Cubs are not a continuation of the amateur Bears because the Cubs are a different franchise. The professional Bears and the amateur Bears are the same franchise. The Cubs lasted for one season and the Hershey Bears' current alternative official name is Hershey Bears Hockey Club. The Hershey Bears' real/official team name is "Hershey Bears" and not "Hershey Bears Hockey Club".