Oyuna is from the Mongolian and Buryat оюун (oyun — turquoise gemstone, also wisdom). Princess Oyuna — modern Mongolian royal heritage naming. Oyuna Erdenebold — Mongolian Olympic athlete. Oyuna Bayasgalan — modern Mongolian-American figure.
Oyuna 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 Oyuna reduce to 4, The Builder. This is a traditional interpretive system, not a factual claim about the name.