Or it is actually also Greek - it means to suckle or get nourishment. Since Byzas is a legendary character who was raised by the spring nymph/naiad Byzia aka "ample breasts". So there must have been a spring there and the colonists suckled at it and thus the name and legend?
Sometimes when a new group comes in and takes over a local name from the previous inhabitants, they modify the name to make it meaningful in their own language. For example, La Jolla, California, supposedly meaning "the pearl" in Spanish, may have been an Indian name which the Spanish colonists modified. So the Greek colonists could have modified a native name in the case of Byzantion.