It is one of the variants of Grace, which is an English name that in Spanish corresponds to Graciela. There is also the variant Greeicy (Name of a famous Colombian singer named Greeicy Rendón). Another variant is Graziz. The name is of Latin origin which means "The one of natural charm, the one that has grace".
It is a woman's name, but its etymology is more than doubtful. It looks like a variant of Grace, which in Spanish is used as Graciela's hypocoristic, just like Gray or Grey; the latter is a surname with variants in the British Isles (Greye; McGraw) who formed a patronymic as Greyson, and who could also end up in Spanish as the name Greysi. Most likely, it is a reference to gray hair, hair color. See English/grey ("grey").
