Esme comes from the Old French esmé, the past participle of esmer ("to love" or "to esteem") — meaning literally "loved" or "esteemed." The name was originally male, brought from France to Scotland in the 16th century with Esmé Stewart, Duke of Lennox.
Esme is now used predominantly for girls. J.D. Today it sits in the U.S. top 415.
Esme 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 Esme reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.