Rose has two origins braided together. The first is the obvious one — the English word for the flower, which in turn comes from the Latin rosa. The second is older and slightly hidden: Rose may also derive from the Germanic name Hrodohaidis, meaning "famous kind" or "famous type," which entered English through the Normans.
Rose was hugely popular in the late nineteenth century, declined through most of the twentieth, and has returned in the past decade as parents reach back for short classical names.
Rose 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 Rose reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.