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If I'm not mistaken, the Sumerians called themselves as 𒊕𒈪𒂵 (saĝ-gíg-ga) and their country as 𒆠𒂗𒄀 (k-en-gi(-r), how would you turn that into an adjectival form or demonym like how -n is added to America to turn it into an adjectival form denoting to the American people, culture, etc.?
Similarly, how would demonyms be formed in Akkadian?
Sumerian has very few words that can be described as "adjectives". Someone's homeland would instead be indicated by just combining nouns: lú adabki "the man from Adab". So if you wanted to talk about a whole population, you could extend this to nam.lú.ulu₃ adabki "the people from Adab". This is generally written without a genitive marker, but I believe the marker should be there in the spoken language even if it's not written.
Most Afro-Asiatic languages would indicate this with a nisba suffix (or as Huehnergard calls it, a "relative adjective"). And indeed, Akkadian has (or at one point had) that suffix too, though it usually gets absorbed into the final vowel of whatever it's attached to: aḫ-um "border" + -ī > aḫ-ī-um > aḫûm "outsider".
Thus, the most common way to form a demonym is (practically speaking) to lengthen the suffix: Amurr-um "Amor" > Amurrûm "Amorite".
