To make a secondary website the primary website for a site collection (which associates the site collection's URL and any of its custom domain names with the new primary website):

1. Go to the site collection detail page.
2. In the Secondary sites in this collection section, find the website that you want to set as the new primary website.
3. Click the website's Make primary button.
   

WARNING: Do NOT delete the "old" site yet. There's still one more step. Keep reading...