They called it Mulu-Babbar (meaning "star of the god Marduk") and recognized it as a wandering star, distinguishing it from the fixed stars. Evidence suggests they observed and charted its movements as early as the 7th or 8th century BC.
However, it's important to remember that ancient cultures around the world likely observed Jupiter, and their observations may predate the Babylonians. We simply don't have the same level of documentation from those early civilizations.