From *ბათომი(*batomi), blend of Ancient Greekβαθύς(bathús, “deep”) and suffix -ომი(-omi), which is a common suffix for Georgian toponyms. Compare თორთომი(tortomi), ცხომი(cxomi).
There are other suggestions, for example, Simon Kaukhchishvili derives the term from Svanბაჩ(bač, “stone”).