That is the correct spelling of the female given name "Rosemary".
(Also "Rose Mary" and "Rose Marie".)
Rosemary in Japanese is ローズマリー (ro-zuma-ri).
Rosemary Lane's birth name is Mullican, Rosemary.
Hope Rosemary's birth name is Hope Rosemary Brown.
Rosemary Rotondi's birth name is Rosemary Ann Rotondi.
Rosemary Squires's birth name is Joan Rosemary Yarrow.
Rosemary West's birth name is Rosemary Pauline Letts.
Rosemary Conley's birth name is Rosemary Jean Neil.
Rosemary Ingham's birth name is Rosemary Anne Gleason.
Rosemary Gearheart's birth name is Rosemary Spence Gearhart.
Rosemary Leach's birth name is Rosemary Anne Leach.
Rosemary Leonard's birth name is Rosemary Anne Leonard.
Rosemary Verey's birth name is Rosemary Isabel Baird Sandilands.