I looked up Dr. W. PAPE’s Woerterbuch der griechischen Eigennamen. Dritte Auflage neu bearbeitet von Dr. Gustav Eduard BENSELER. Vierter Abdruck. Braunschweig, 1911, the big old Greek dictionary of proper names. The best it had to offer is Suda’s gloss of the noun thisbē as ‘funerary urn’ (σορός): SOL Search.
The Thisbe mentioned by Ovid (Pyramus and Thisbe) was supposed to be from Babylon, which makes one suspect an Eastern origin for the name; but Thisbe was already used in ancient Greek, to refer to a nymph, and a town named after the nymph in Boeotia: Boeotian Naiad Nymph of Greek Mythology (town mentioned in Iliad 2.502). That makes it likelier that something like “urn” was the origin of the town name, and the nymph name was retconned.
Thisbe – Meaning of Thisbe says that the name means “where the dove lives”. This is a misunderstanding of πολυτρήρωνά τε Θίσβην “Thisbe of the many doves”, the description of the town in the Iliad.
Thisbe is the Septuagint transliteration of the town of Tishbe in Israel; a term which in Hebrew means ‘captivity’.