Erdene is from the Mongolian эрдэнэ (erdene — jewel, treasure, precious). Erdene Ochir — modern Mongolian-American figure. Princess Erdene — modern Mongolian royal heritage naming. The Mongolian-American community has continued to preserve Mongolian heritage names through cultural centers including the Mongolian American Cultural Center in Arlington, Virginia.
Erdene 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 Erdene reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.