The grammar here is not particularly straight forward. So, for anyone just starting Latin, "mihi" is not always "my" (which is more accurately the possessive adjective "meus, mea, meum")
"mihi" is the dative case of "ego" (I). So, while the given translation is perfectly good, if you are trying to understand it literally it is something like "The name to me is Marcus."
Is the aspiration of the -h- in mihi correct according to the classical pronunciation? I am honestly asking because I don't know.