I found this sentence "Silvia stieg aus dem Taxi und ging zu Jochens Haus." in a short story book. Wouldn't it be better to replace zu with nach?
Nach is used to indicate a direction with names of cities, countries and the like when they do not have an article.
Wir fahren nach Paris, Frankreich, Bayern.
In is used with names where the article is obligatory.
Wir fahren in die Schweiz, in die Bourgogne.
Nach is also used as a fixed expression with Hause to indicate movement toward someone's home. As a fixed expression, Hause must occur alone and cannot be accompanied by any other word (e.g. no article, not prenominal genitive such as Jochens).
Ihr könnt nach Hause fahren.
Zu as a directional preposition can be combined with nouns indicating people or places. In this case, an article must be present.
Ich muss zum Arzt, zur Post, zu Jochens Haus.
The final piece of the puzzle is that a prenominal genitive such as Jochens is equivalent to a definite article. Therefore, Jochens Haus fits zu but not nach for the reason mentioned above.
With names, no article is required.
Geh doch zu Dr. Piegsa.
Sounds similar, but has different meanings:
zu Hause → at home
nach Hause → home (direction)
das Zuhause → the home
zu Jochens Haus → to Jochen's house/home
While the two are interchangeable in English they're not in German. In colloquial German you might even say zu Haus, nach Haus, because the -e at the end is actually a historic form and already dropped in many other words (e.g. am Grabe → am Grab, zu Gemüte → zu Gemüt).