The citizens of Sparta, grateful for the successful return of Helen by the help of an Athenian man named “Academus” purchased a grove on the outskirts of Athens and gave it to him. Much later the grove became a public garden known as The Grove Of Academus. Circa 387 B.C. Plato, the Athenian philosopher took up his residence adjacent to the garden. As the young men of Athens came to study with him it was his habit to teach them as he walked the paths in the garden. This was his practice for the next 40 years. It is no wonder then that the Athenians named Plato’s school “the Academia” Source
History would tell the rest of the story and down through the ages we have received the word Academy as an institution of concentrated learning.
Through a series of associations one thing became named for another. Thus we read in Acts 11:26 that the disciples of Jesus were first called “Christians” Antioch. The word is not meant to be a complement and may not have been used in a derogatory fashion either. It was already common to name groups in this manner. Hence followers of Herod were Herodians etc.