I can see why you are confused! The question literally translates to "Do you still have hunger?". So in Finnish we usually say that we have hunger instead of being hungry.
We don't have a separate verb "to have" in Finnish. So we express it like this: personal pronouns (minä, sinä, hän, me, te, he, se, ne) in adessive case + "on" (olla-verb in 3rd person singular). It's always "on", no matter who owns or what they own
Here's a good explanation of the possessive if you want to read more: https://uusikielemme.fi/finnish-grammar/syntax/sentence-types/possession-having-something/