An Americanized pronunciation would probably be something along the lines of Mag-lee-ozzey.
However, if you use the correct Italian pronunciation, it would indeed be something like, “Mawl-yaht-zee”.
Americans tend to screw up the pronunciation of many foreign names, with Italian ones being among the most frequently mispronounced. As a result, some people just give up and use the Americanized pronunciation for their own name, even though it is incorrect.
As an example, an old friend of mine has the last name, Vigneri. Even though he has lapsed into pronouncing it, “Vig-nary”, the correct pronunciation is along the lines of, Veen-yary.
Sometimes it is just easier to go along with the incorrect masses, rather than to keep trying to correct them, I suppose.