Count: 0. No stars with IAU‑approved proper names begin with the letter O. Present this as a focused reference: the list is empty under the strict criterion of IAU‑approved or well‑established traditional proper names. Note an interesting detail: many catalogued names that look like they start with O are actually Bayer designations using the Greek letter Omicron (ο), or are parts of constellation names such as Ophiuchus and Orion, not standalone proper names for individual stars.

Understand why the strict search yields nothing. Rely on the IAU Working Group on Star Names and standard catalogs (SIMBAD, Bright Star Catalogue, Gaia releases) as the authority: the IAU’s approved name list and major catalogs simply do not include a proper‑name entry beginning with O. Expect common near‑hits instead — Bayer names like Omicron Tauri, spectral class O stars (a temperature class, not a name), or transliterated traditional names that sometimes begin with other letters when standardized. Use related searches instead: look up stars in constellations that start with O (Orion, Ophiuchus), stars whose proper names contain the letter O, or consult the complete A–Z index of IAU‑approved names for nearby alternatives.