Klymene (Κλυμένη) is the Greek word for "famous" or "renowned." An Oceanid daughter of Tethys — mother of Phaethon by Helios.
Also a Nereid in some traditions.
Klymene 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 Klymene reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.