In Don Giovanni, Don Ottavio apparently lives with the Commendatore and Donna Anna. According to the stage directions, as the Commendatore challenges Don Giovanni to their fatal duel, Donna Anna runs back into the house, and then comes out (too late) with Don Ottavio. And her claim that she mistook Don Giovanni for Ottavio when he came to her chamber late at night makes the most sense if Ottavio was already in the house.
Unless someone can give me a better explanation, I'll assume that Ottavio is the Commendatore's ward.
In the medieval and Renaissance eras (and Don Giovanni is obviously meant to take place earlier than it was composed), aristocratic boys were often fostered with other noble families, to secure the alliance between the families and to supposedly build better character by preventing the boys' own parents from spoiling them. Sometimes this practice led to marriage with the foster family's daughter. It seems likely to me that this is Ottavio's situation.
If this is true, then maybe it explains a lot about both Anna and Ottavio's behavior throughout the opera, especially Ottavio's, and especially if both are portrayed as very young. Not only does Anna lose her father, but Ottavio loses his foster father. (Although he doesn't seem to grieve for him much, but focuses all his emotions on comforting Anna – the Commendatore must have maintained a formal distance from him.) Until this point, neither one has lived as an independent adult; they've both been under the Commendatore's authority. But suddenly, in an especially brutal and (for Anna) traumatic way, they're thrust into adulthood.
Suddenly they're the ones in charge and need to make all the important grown-up decisions. Their inexperience and unpreparedness might explain a lot about them. For example, why sometimes Anna is the one who calls for revenge on her father's killer and urges the more cautious Ottavio forward, while at other times, due either to fear or the weight of her grief, she falters and Ottavio takes the lead in their revenge quest. Or just why Ottavio is so cautious and reluctant to accuse Don Giovanni of the crime in the first place, and his sheer naïveté in thinking the culprit couldn't possibly be an aristocrat. Or their disagreement on whether to seek comfort by marrying straight away or delay their marriage to mourn the Commendatore's death.
All these things have been explained in many different ways by different opera scholars, stage directors, singers, etc. But viewing Anna and Ottavio as effectively two children, forced to grow up too quickly by the loss of their mutual father figure, makes a good amount of sense to me.
