America is the feminized form of Americus — the Latin form of Italian Amerigo from the Old Germanic amal (industrious, work) + ric (ruler). The continents were named after the Florentine navigator Amerigo Vespucci (1454-1512), who first proposed in his 1503 letters that the lands Columbus had reached were a new continent rather than the East Indies.
America 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 America reduce to 5, The Seeker. This is a traditional interpretive system, not a factual claim about the name.