Yes, hosting your domain on a VPS without purchasing a domain name is possible by using free subdomains provided by services like No-IP or DuckDNS, using the VPS's IP address directly, or registering a free domain through services like Freenom. You can then point the free subdomain or free domain to your VPS's IP address, configure your web server (such as Apache or Nginx) on the VPS to serve your website and access your site using the chosen subdomain, free domain, or IP address.