Clearly, a name (human or divine) in the Genitive should be restored before εἰμὶ. The graffito ran the circumference of the foot, and the surviving fragment represents about a quarter segment of the circle, there is therefore a lot of available space to fill between Βακ[- -] and εἰμὶ. I am inclined to read Βακ[- -] as the start of a personal name, e.g. Bakis attested at Pantikapaion in the 4th cent BCE (LGPN V4-16481) or Βάκχιος attested at Olbia-Borysthenes (LGPN V4-16491 = Dubois, IGDOlbia 110, 2, II century B.C.E.), as well as at Gorgippia (LGPN V4-16490) in the III century CIRB 1137 B II, 38). In the IV century, we have one Βάκχων at Olynthos (LGPN V4-26252) ca. ?355 B.C.E. To fill in the available space I would, e.g., restore [Ἀπολλώνος] εἰμὶ. Βακ[e.g.-χιος μ’ἀνέθηκεν.]

It would be tempting perhaps to speculate another possibility, that of the poetic epiclesis of Dionysos - Bakcheios. Βάκχειος Διόνυσος is mentioned in the Homeric Hymn to Pan, line 46. At Olbia Pontica, in the V century B.C.E., we may have had a cult of Διόνυσος Βάκχειος: according to Herodotus 4.79, Scythian king Skyles took part in the celebrations (telete) of Dionysos Bakcheios at Olbia. It is therefore possible that on Berezan, this cult was also known, or a resident of Berezan may have been a participant in the celebrations of Dionysos at Olbia and prepared (inscribed) a cup for a dedication to be made at Olbia, but failed to deliver it. In the case of the cultic epiclesis, we could restore the inscription as e.g. Βακ[χεῖο Διονύσο ἱερὴ/ἱερὸς/ἱερὸν] εἰμί. I have added ἱερὴ/ἱερὸς/ἱερὸν as there seems to be more space availabe around the circumference than would be necessary just for the cultic names.