Do I need web hosting if I own my website?

Yes. Owning your website means you own the files, the design, and the code, but those files still need to live on a server somewhere to be visible online. Ownership and hosting are two separate things: one is about who controls the asset, the other is about where it physically runs.

When you own your site outright, you can choose your own hosting, bring your own host, or use hosting that's included as part of what you're already paying for. Either way, hosting doesn't go away just because you own the site.