In Spanish, the spelling is not optional (in some cases, there are two correct options) and that is valid for words and for names. So, Rosío is just a misspelling of Rocío and Moncerrat is a misspelling of Monserrat, a variant of Montserrat, from the Catalan Montserrat.
That said, C (+e, i)/Z and S (+e, i) sound the same in American Spanish and in some European Spanish dialects (Canarian and some areas of Andalusian) but they have two absolutely different sounds in Castilian Spanish (C +e, i and Z sound like the English TH in "think").
The letter X is pronounced depending on this position: at the start of a word (xilofono) it sounds like S; between vowels, it sounds like KS (examen, éxito); between a vowel and a consonant (expandir) it sounds KS or S depending on the dialect, the speaker... Besides the general rule, in some Mexican names and words from Nahuatl origin it represents the sound SH (Xola, mixiote). Finally, in some place names (Oaxaca, México, Texas) and in some family names (Ximénez), the X retains the historical sound [x] (KH). Some of those place names can even be spelled with J (México/Méjico, Texas/Tejas).
The groups TX and TZ don't appear in Spanish.
So Yulixa (and Yulitza) would never be correctly pronounced the same that Yulisa. According the rules (mandatory for ALL the speakers of ALL the dialects in ANY country, region, area...), Yulisa is pronounced with S and Yulixa is pronounced with KS. Yulitza would not be a Spanish name because of the TZ, which must be pronounced like a T and a TH/S (depending on the dialect).
Among poor educated or uneducated American Spanish speakers, it is not unusual to use Z/TZ/TS/TX/C/CS/XS... as variants of S, specially in the ending -isa (used as sufix to create new names in some American areas). Even if Z/C could legitly the same pronunciation of S, they are not interchangeable (the groups TZ and so on are simply not possible in Spanish).
In Spain, among poor educated or uneducated people, it is some times possible to find S/C/Z mixed up (never with X or TZ/TS/TC...) in recently appeared names, mainly in foreign names, but the misspellings are not so common as in a lot of American countries, probably because of the existence of naming laws and higher levels of education (the same is true for Argentina, Uruguay and Chile).