"Miikka, do you have a Finnish name?"
Translation:Miikka, onko sinulla suomalainen nimi?
Nimi is a countable noun. When a singular countable noun is the thing possessed in a possessive sentence, it's nominative.
If it were an uncountable noun like mehu, positioned after the possessor as in this sentence, then it would be partitive.
So 'Onko sinulla suomalainen nimi?', but 'Onko sinulla suomalaista mehua?'
EDIT: In existential/possessive sentences beginning with onko followed by the location/possessor, sometimes even countable nouns are partitive, as in 'Onko sinulla pipoa?' This is discussed in the Tech tips, and some more here.
I think in the sentences currently in this course, the countable subjects of such sentences are almost all nominative when preceded by an adjective, but partitive when alone.