As someone who's firmly in the /maɹiəʊ/ "cat" camp, it's weird how people (Americans in particular) consider this pronunciation wrong yet have no problem with "Maria." I assume "Maria" is just the feminine form?
Are you British/speak British English? In standard American English, Mario is rendered like MAR-io [‘mɑː.ɹi.joʊ̯]. British English is more like MARRY-o,, which I've seen rendered as [‘ma.ɹi.jɘʊ̯] (which looks like the traditional version of what you included?), but it's still less flat of an "a" sound than when Americans tend to do the "marry-o" pronunciation.
And you say Maria with the same "a" sound as is mat, bat, cat? That delays and hardens the r sound, which - in American English - isn't a typical pronunciation, which is closer to muh-'ree-uh or mer-'ee-uh ( /məˈriːə/).
It's pronounced differently than Mario because the stress is on a different syllable, and stressed syllables in English are higher, longer, and louder, so the "a" in Mario is "bigger" than the "a" in Maria.
Why stressed on different syllables? In Italian, there's an accent on the "i," in Maria, meaning the -ia at the end is separated into two distinct syllables, whereas the -io in Mario is basically a dipthong and closer to a -yo sound together. Why did they add an accent? No idea. I've read some comment that Mario and Maria actually have different language origins (straight Latin (
Marius)for Mario, vs Hebrew through Greek and Latin for Maria), so that might be related: "
Maria (
Greek: Μαρία) is a form of the name used in the
New Testament, standing alongside
Mariam (Μαριάμ). It reflects the
Syro-Aramaic name
Maryam, which is in turn derived from the
Biblical Hebrew name
Miriam. As a result of their similarity and
syncretism, the Latin original name
Mariaand the Hebrew-derived
Maria combined to form a single name." - wiki explanation of the etymology