Imogen first appears in print in Shakespeare's Cymbeline (c. 1610) — possibly a printer's error for Innogen, an older Celtic name from inghean (Old Irish) meaning "maiden" or "girl." Shakespeare's heroine is one of his most fully drawn women; the critic William Hazlitt called her "the most tender and the most artless" of all his characters.
Imogen is hugely popular in the United Kingdom (in the top 50) and Australia. In the U.S. it entered the top 1000 in 2007 and has been climbing. The British actress Imogen Poots and the singer Imogen Heap are well known. Today Imogen sits in the U.S. top 600 and is climbing fast.
Imogen 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 Imogen reduce to 9, The Giver. This is a traditional interpretive system, not a factual claim about the name.