What does Ximena mean?
An old Iberian name (also spelled Jimena; the archaic X represents the sound later written J) of genuinely uncertain origin. The main theories derive it from the Basque seme 'son', or treat it as a feminine of Simon/Simeon (Hebrew Shim'on, 'he has heard'). Neither is settled. Famous as the wife of El Cid.
What does Carmen mean?
A Marian devotional name from the title 'María del Carmen', Our Lady of Mount Carmel. Carmel comes from the Hebrew karmel 'garden, orchard, vineyard'. By coincidence the identical Latin word carmen means 'song, poem', which has reinforced the name's appeal.