What is the meaning of the name "Rumaysa" and is it permissible to name a child with it, knowing that it is the name of a female Companion [of the Prophet]?

No female Companion with this name has been found. It is most likely that the intended Companion is the eminent female Companion Umm Sulaym bint Milhan, whose real name was Sahla, or Unayfa, or Rumaytha. As for the name "Rumaysa," it is likely derived from "al-rams," meaning burial, and it is not advisable to use it for naming.