Why was Madison Square Garden called a 'garden?

The "building" was an oval arena with brick walls and no roof. In 1875 the famous bandmaster Patrick Sarsfield Gilmore (composer of the song "When Johnny Comes Marching Home") obtained the lease and opened Gilmore's Garden. The bandleader converted the space into a garden with flowers, trees, and waterfalls, and held promenade concerts there. In 1879 William Vanderbilt regained control of the property and changed its name to Madison Square Garden.

this sounds convincing

Actually the Word garden has many definitions, two of which are, "an open air eating or drinking place" and "a large hall for public entertainment". Origin of the world is from French and German.