I love the way this name sounds--I actually like it much better than the more common (and like-sounding) Renee. Although, I have a feeling that if I ever used it, I would encounter the same confusion as the above poster has.
I think Remei must be a Marian Name, a cognate of the Spanish name Remedios which itself comes from a title of Mary, mother of Jesus: "Our Lady of the Remedies" ("Nuestra Señora de los Remedios", in Spanish); in Catalan, it's "la Mare de Déu del Remei" (literally "the Mother of God of the Remedy"), sometimes "Nostra Senyora del Remei" ("Our Lady of the Remedy"). [noted -ed]