Domna is from the Latin domina (lady, mistress), or possibly the Aramaic root dmm (black). Julia Domna (160-217 CE) was the Syrian-born empress of Rome — wife of Septimius Severus, mother of Caracalla and Geta.
She supported Philostratus's biography of Apollonius of Tyana.
Domna 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 Domna reduce to 2, The Peacemaker. This is a traditional interpretive system, not a factual claim about the name.