Dorothy comes from the Greek Dōrothea (Δωροθέα) — dōron (gift) and theos (god) — meaning "gift of God." Theodora has the same elements in reverse.
Dorothy was the second most popular U.S. girls' name from 1925 to 1929. Dorothy Gale in The Wonderful Wizard of Oz (1900) is the most enduring fictional bearer. Today Dorothy is returning, sitting in the U.S. top 500 and climbing fast.
Dorothy 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 Dorothy reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.