If you've searched you platform's app store, then you'll know that we don't have a native app. There are good reasons for this, which we'll get into later, but there is still a way that you can use Wheel of Names offline by launching it through an icon on your home page, without having to navigate to wheelofnames.com through your browser.
To add a Wheel of Names icon to your home screen, you can open your browser's menu while on wheelofnames.com, and find the option there labelled something like "Add to home screen" or "Add shortcut".
However, if you want it to work offline, you need to install it as a "progressive web app" (PWA). That's currently only possible in Chromium-based browsers like Google Chrome. In those browsers, the option should be labelled "Install app", or something similar.
When using the app offline, some functionality will be limited. You won't be able to save or open wheels in the cloud, but local file saves will still work. Sharing wheels and viewing shared wheels will not work. During- and after-spin sounds and images that you haven't previously loaded while online will not load.
As for why we don't have a native app, it is mostly a matter of the time we have available. Making a true native mobile app is completely out of the question for us, as we'd need to develop and maintain (at least) three completely separate client code-bases in completely different languages.
Theoretically, it would be possible to create an app store app using our existing client code-base using a technology called Capacitor, but it's not a drop-in solution, and would require some large changes. It just has not been a high enough priority for us to dedicate time to develop it.
In the future, it's possible that we may be able to expand PWA functionality to non-Chromium browsers, but support on the browser and operating system levels varies greatly. For now, we are choosing to focus on fixing bugs and adding features.