Han is from the Korean Han (한 — one of the most-common Korean surnames) and the Vietnamese Hân (joy, happiness). Han is one of the Korean surnames — historically associated with the Cheongju Han clan, one of the noble Korean clans descended from the ancient Mahan kingdom. Also Vietnamese: Hân as feminine name expressing joy.
Han 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 Han reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.