ΛΗΝΑΙΟΣ should most likely be read as a personal name Λήναιος, so listed in LGPN online (V4-19514), marking the pot as his property. The name is followed by a probable alpha (or a lambda with an accidental horizontal stroke that extends far to the left beyond lambda's left diagonal) and quite a clear circle, which should presumably be read as an omicron, so I print ΑΟ, but the meaning of these last two letters is unclear. The circle that follows alpha does not have legs and therefore cannot be an omega, unless we are dealing with Attic script, which is not likely here. There might be a letter (diamond-shaped?) between the iota and omicron of ΛΗΝΑΙΟΣ, unless the strokes are accidental. In fact, the whole graffito is very messy: there are many double strokes and slips of the writing tool. The surface, while convex, was not so difficult for writing, and the writer had to be either inexperienced or with their hand unsteadied (by drink?).

Tolstoy (1953, no. 75) preferred to read ΛΗΝΑΙΟΣ as an adjective ληναῖος derived from the festival Λήναια and to interpret the last letter on the right as a lunate sigma, restoring the whole text as ληναῖος ἀσ[κός]. At the same time, he mentioned T.N. Knipovich's view that the use of lunate sigma could be seen as too early for the proposed date of the cup (late V - early IV cent. B.C.E.), which would also be my objection. Apparently, Knipovich was inclined to read the last letter as either omicron or theta. Yaylenko (1980/2, p. 90. no. 19; SEG 30.883) read the text as Λήναιος Ἀθ̣(ηνᾶι?), and Dubois (IGDOlb no. 70) as Λήναιος Ἀθ̣(ηνάηι) "Lenaios to Athena". They both see the graffito as dedicatory.

Λήναιος as a personal name derives from the name of the month Ληναιών, which was an Ionian, not an Attic month, and was specifically a Milesian and Olbian month, so we should perhaps lean towards expecting the writer to be Ionian and using the Ionian alphabet. At least six more individuals bearing this name are attested at Olbia-Borysthenes; in my view, it is not certain that we should assume the two attestations of the name on a bronze mirror (dated ca. 500 BCE, found in a burial at Olbia) to be references to the same person, that is, that Λήναιος Δημοκλō was the father of Δημώνασσα Ληναίō, also mentioned on that mirror (IGDOlb no. 92; Dubois interprets these two as father and daughter), and LGPN accepts these attestations as referring to one individual (V4-19515). If that were the case, it would be unusual for the daughter's name to precede the father's as family members typically appeared in inscriptions in generational and senioral sequence.

Ληναῖος is also a cultic epiclesis of Dionysos, and we could conceivably see a dedication here, in the Nominative form of the theonym. Also conceivable is that the epiclesis could be read in the Genitive, Ληναῖο, followed by Σαο(?). Yaylenko thought the inscription may have been left unfinished, which is a distinct possibility. On the worship of Dionysos at Olbia and on various Dionysic festivals, such as Lenaia, see Rusyaeva (1979, 72-91).