While it’s not possible to manage your domain from the mobile app, you can add a custom domain from the browser by logging in to WordPress.com/login and going to Manage > Domains > Add New and follow the steps to register a new domain.
Please note that using a custom domain requires at least a Personal plan. You can register a domain without a paid plan but you will only be able to use it as your site’s primary domain with an upgrade to one of our paid plans.
Once your domain is registered, you can set it as primary on your site and your old domain will now redirect to the custom domain added. Your Primary domain, or site address, is the site address people will see in their browser’s address bar when they visit your site.
If instead of adding a custom domain you want to change your WordPress.com subdomain. Click on the subdomain from Manage > Domains instead of Add New and you’ll see the option to rename this here address once it’s selected.