Damo (Δαμώ) is the Greek mythological short form. Damo (6th c. BCE) was the daughter of Pythagoras and Theano — entrusted with his secret writings, she refused to sell them despite living in poverty in obedience to her father's wishes. A model of Pythagorean fidelity.
Featured in Diogenes Laërtius's Lives of Eminent Philosophers.
Damo 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 Damo reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.