When someone finishes Hajj, he/she is called Haji (though it is not to be used as a show-off). When someone leads the Salat, he is called Imam.
So, if someone finishes reading (not memorizing) the Quran thrice, is he/she given any title?
Also, a Hafiz is one who memorizes the Quran. So, what do we call someone (non-Arab) who memorizes the Quran "with" meaning?
(Though they can all be called "Muslim who is doing his job")