Rosamund is from the Germanic hros (horse) + mund (protection) — "horse protector"; later folk-etymologized as Latin rosa mundi (rose of the world). Fair Rosamund (Rosamund Clifford, c. Princess Rosamund — English heritage naming.
Rosamund is a compound name. Its parts are mund — each an attested element with a recorded meaning of its own.
Rosamund 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 Rosamund reduce to 6, The Nurturer. This is a traditional interpretive system, not a factual claim about the name.