When choosing and purchasing a domain to use with the custom domain feature, you cannot use the Kartra brand name, whether for your own business or for affiliate use. See Section 11.1 Intellectual Property in the Terms of Service.
The above does not apply to your pages created using Kartra Pages without a custom domain integration. Those URLs will all automatically contain Kartra. The format of those pages is https://username.kartra.com/page/pagename