A pretty name. Retro chic really and due for a revival. If people can call their baby girls names like Florence and Elsie and that's apparently fine, then why not skip forward a few decades to Rosemary?
The meaning is 'dew of the sea' apparently from rose + marinus, so it's not just a combination of Rose + Mary as you would assume. Like all the Rose- names, it's lovely, and Rose or Rosie could be used for short.