Tῶν μετρίων τοὔνομα means literally "the name of the measured/moderate things" — in other words, as you say, "the middle way," "the mean," "moderation." The "mean" was first (according to ancient tradition) touted by one of the Seven Sages, the tyrant Cleobulus of Rhodian Lindos, back in the sixth century B.C.: Μέτρον ἄριστον, said he — "The measure (mean) is best." The sentiment was seconded on the temple of Apollo at Delphi, where μηδὲν ἅγαν ("Nothing too much") was inscribed as a companion to "Know thyself." Those became the two perennial "mottos," as it were, of Greek civilization itself. We should probably note that societies usually extol the very virtues that are apparently most lacking in themselves.
Pronunciation of τῶν μετρίων τοὔνομα (literally, "of the moderate things the name"): toan meh-tree-own too-no-mah.
Pronunciation of τὰ μέτρια ("the moderate things"): tah meh-tree-ah.
Pronunciation of τὸ μέτρον ("the measure," "the mean"): toh meh-tron.