Meaning
(1) a Greek rhetorician or
(2) a Jewish rabbi.
(1) This is the common opinion, and many identify him with a certain Tyrannus, a sophist, mentioned by Suidas. Paul would thus appear to be one of the traveling rhetors of the time, who had hired such a hall to proclaim his own peculiar philosophy (Ramsay, Paul the Traveler, 246, 271).
(2) Meyer thinks that as the apostle had not passed wholly to the Gentiles, and Jews still flocked to hear him, and also that as Tyrannus is not spoken of as a proselyte (sebomenos ton Theon), this schole is the beth Midrash of a Jewish rabbi. "Paul with his Christians withdrew from the public synagogue to the private synagogue of Tyrannus, where he and his doctrine were more secure from public annoyance" (Meyer in the place cited.).
(3) Another view (Overbeck) is that the expression was the standing name of the place after the original owner.
S. F. Hunter