Rose? Not Rose.
Learned something from World Wide Words today. The name "Rosemary" is a reanalysis of ros marinus, ocean dew (the herb's original name).
I already knew that "Rosamund" wasn't rosa mundi, rose of the world, but instead hros + mund, horse-shield (compare Edmund, Raymond, Siegmund). "Rosalind" and its variants are not rosa + linda, lovely rose but instead hros + linde, tender horse (although in both of those cases it's probably not accurate to think of them as meaningful compounds; they're more likely to be simple combinations of elements used to make names).
And of course, a number of Rose- names in English originally came from the Germanic hrod, fame - the name was around long before the flower came to England. An example of that is "Roswitha", hrod + swinþ, fame-strength. "Rose" itself began life in England as "Roese, Rohese", from hrod + heid, fame-kind, though Latin "Rosa" probably contributed to its rebirth as a popular name.