The name Rumi is a girl's name of Japanese origin meaning "beauty, flow, lapis lazuli". Rumi and is often added to lists like Cool Girl Names From Around the World and discussed in our forums with posts like "Pick 5 (GIRLS)".
From the experts:
Rumi is a Japanese girls' name that sounds like a couple of other choices more familiar in the West -- Rumer and Remi -- that is achieving notice because of its choice by two celebrities, including Beyonce and Jay-Z. Rumi is perhaps best-known as the name of a (male)13th century Muslim mystic and poet whose most famous poem, "The Diver's Clothes Lying Empty", has inspired many modern literary works, including Vendela Vida's novel with a nearly-identical title. There are also several notable Japanese women named Rumi.