"Kodratrou Dometiou" is the genitive form of two saints names, Kodratos and Dometios respectively. The names are not accompanied by the title "Agios" or "Saint," which could indicate a relatively early date, since in the middle and later Byzantine period, saints were consistently addressed with such nomenclature. The vessel was perhaps used in a liturgical context in a church in which both saints were venerated.
For a single-handled jug of similar style, also with incised herringbone on the shoulders, see no. 57 in H.C. Evans and B. Ratliff, eds., Byzantium and Islam, Age of Transition.