The name derives from "Evlalos", an epithet of god Apollon in Greek religion. The feminine form "Evlalia" (Eulalia) was a very common Greek name in Ancient Minor Asia.
Olalla and Lalla are Spanish diminutives of Eulalia. According to some sources Eulalia, so popular in Spain, was introduced into England during the Middle Ages, and was mispronounced as Hilaria. Such sources see Hilaria during the Middle Ages as a form of Eulalia rather than a feminine form of Hilary.
Saint Eulàlia (ca. 290-12 February 303) is the patron saint of Barcelona, where as a Christian she suffered martyrdom during the reign of Roman emperor Diocletian.
I fell in love with this name the first time I saw it when I was twenty years old. It was the name of one of the poets in some Spanish-language poetry anthology my Spanish class was using. I like the European and Latin American pronunciation Yu-LAHL-ya, and the nickname Lally. It's one of my most favorite female names.
Wow! One would really have "to talk well" to pronounce this name with ease! It sounds like a tongue-twister. Too many vowels and Ls. Other than that, it's not the worst name out there.