Abdul comes from "Abd": servant of. Not muslim.
Murat mean "wanted", "desired", "wished". Not muslim.
Alim means "scholar". Not muslim.
Etc... A lot of these names are just Arab. Not all of them, I agree, but muslim and arab(ian) are two different things (remember that the big majority of the muslims in this world live in Indonesia and Africa and are not Arabs). And I don't find that very strange given that a lot of Westerosi names are christian (Jon, Lysa...), or directly taken from real cultures (Robert, Arya...). Generally the names and words in GRR Martin's universe are not very exotic (except for the Valyrian and all the magic features).
The problem is more with the lack of informations about the Yi Ti. Are there attested Yi Ti names in the books? Three cities: Asabhad (Persian/West-Indian like), Yin (Chinese like) and Jinqi (northern Chinese like, perhaps Manchu). Yi ti is probably a transposal of the amalgam of all these eastern cultures that made the western europeans dream (= the eastern cultures of the silk road).