Not yet, but it's on our roadmap ✔️🗒️. In the future, we plan to give app creators the ability to find/buy a domain to tie their app to.
If this is a request you'd love to see, please upvote the existing request in the feature-request channel on our Discord.
A temporary stop-gap solution would be to:
After purchasing your desired domain, (E.g. CookingRecipes.ai), navigate to your domain portfolio, and choose to "forward" your domain from the action menu. Here's an example of how this can be done with a registrar like GoDaddy: https://www.godaddy.com/help/forward-my-godaddy-domain-12123
When selecting the "forwarding type", select "Forward with Masking". Forward with masking sends visitors to your domain over to the destination URL, but keeps your domain in the browser address bar. It also gives you the option to enter meta-tags for search engine info. You can see the differences between just forwarding, and forwarding with masking, here on this article.
Now when a user visits your domain, for example CookingRecipes.ai, it takes them to your brancher.ai app!