Rumi has parallel origins. In Persian, it is the byname of the 13th-century Sufi poet Jalal al-Din Muhammad Rumi (1207-1273), meaning "the Roman" (referring to Anatolia, then under the Roman/Byzantine cultural sphere). In Japanese (留美) it means "beauty" or "lapis lazuli."
Rumi entered the U.S. The Sufi poet remains one of the most widely-read poets in the English-speaking world.
Rumi does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
—
In Pythagorean numerology the letters of Rumi reduce to 7, The Seeker. This is a traditional interpretive system, not a factual claim about the name.