Rimsky is both a surname and a given name. Notable people with the name include:
Nikolai Rimsky-Korsakov (1844–1908), Russian composer
Andrey Rimsky-Korsakov (1878–1940), Russian musicologist and son of Nikolai
Nicolas Rimsky (1886–1941), Russian-born French film director and actor
Voin Rimsky-Korsakov (1822–1871), Russian navigator, hydrographer, and geographer
Rimsky Yuen (b. 1964), current Secretary for Justice of Hong Kong