"Kaʻiulani is her name."
Translation:ʻO Kaʻiulani kona inoa.
Hawaiian doesn't have a verb "to be", so there are a few different ways to create sentences that have different kinds of equivalencies which would be represented by "to be" in English. When equating two nouns one way to do it is with an 'O sentence. The formula 'O translates as " is ."
Also note that proper nouns (i.e. names of people and places) usually require an 'o in front of them, so if we were to switch the order of the nouns it would be: 'O kona inoa 'o Ka'iulani.