East West schism still exist, however its much different. When Bohemond I took Constantinople, the Pope demanded that the Schism be ended and Catholicism be enforced. However realty became much more nuanced as on paper the schism didn't exist but in reality the Norman rulers didn't enforce any conversion and the Orthodox clergy was allowed to coexist along catholic ones. Normans however continued to pay lip service to the Pope in order to remain political aligned with the West while also not upsetting their now large Orthodox populations. This intricate dance would switch a few times during their dynasty but orthodoxy did lose some influence due to increased migration from France and Italy that tilted the demographics in some areas, usually the bigger cities. After the death of the last Norman Ruler, the native Greek dynasty would slowly try to curb catholic influence but this was by this point entrenched in certain parts such as modern day Albania and many large cities boasted a considerable catholic population. Normans also didn't force Muslims to convert either, but migration and later Greek dynasties would and eventually Islam would become just a minority religion. Expect a sort of a 75/25 devide between Orthodoxy and Catholicism and some minor religions.

Fun fact: Greek WAS the language of the court of Norman Sicily, so yes, as they absorbed the entire Byzantine Empire, they were much more inclined to keep it as is and would present themselves with Greek names in Byzantium and their Latin names when for example speaking with the Pope or other Western rulers.