1. Only use 's when you refer to animals, people or groups of people:
- the cat's meow
- the nurse's purse
- Max's mice
"Alba's House Cooking" is incorrect because "Alba's house" is better for the actual living space of a woman named Alba. It does not refer to the dynasty of the Duchy of Alba. For that, you need the preposition OF. "The Cuisine of the House of Alba" is appropriate. As a native speaker, "Alba's House Cooking" makes me think that Alba's apartment has some kind of special powers. (Bad one, Westin Hotels.)
We use 's to talk about:
- a person's possessions (Mike's bikes)
- where a person works (Dad's office)
- a part of a person's body (Bree's knees)
- personal relationships (my father's girlfriend, his sister's boss)
Items, things and buildings cannot, however "own" things (the front door of the block of flats, the back door of the car, the front page of the newspaper)