Bethan is the Welsh diminutive of Elizabeth — from the Hebrew Elisheba, meaning "pledged to God." The name took on its present form in 19th-century Wales.
Bethan is widely used in Wales.
Bethan 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 Bethan reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.