Day \day\ as a girl's name (also used as boy's name Day), is of Old English origin, and the meaning of Day is "day". Possibly use of the word as a name, or originally a surname.
Baby names that sound like Day are Da-, Dai and Daya. Other similar baby names are Bay, Dacy, Kay, Cay, Daly, Dany, Davy, Fay, Gay, Jay, May and Ray.