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A term for that concept, by the way, is "endonym":

Wikipedia says it's "Malti"

Il-Malti to be precise. Il- means "the" and changes its meaning to that of the language. Malti alone would mean a Maltese person.

Source: I'm also Maltese.

The "Il" in Il-Malti is like "al" in Arabic, which Maltese is closely related to as was pointed out above.

Arabic (language): al-‘arabiyyah (الْعَرَبِيَّة).

'ish' is a pretty universal english suffix. So Spanish is just "españ-ish".