You don't necessarily need your own domain, as you get a free subdomain. However, this does not represent a good solution for a serious website. Elementor does not currently offer registration services, but there are many registrars on the market, such as NameCheap, Domainfactory, Host Europe and Google Domains (unfortunately not yet available in Austria), that you can use for this purpose. You can then easily connect your custom domain to your Elementor Cloud website via the My Elementor dashboard. You can find a detailed explanation in the article about adding your custom domain.