Aspen is the English name for the trembling aspen — the white-trunked tree of cold northern forests whose leaves quiver in the slightest breeze. The town of Aspen, Colorado is also famous, and the name carries a hint of both the tree and the mountain resort.
Aspen as a girl's name is recent, entering the U.S. top 1000 in 2007. Today it sits in the U.S.
Aspen 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 Aspen reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.