Yes! Self-hosted WordPress requires that you rent the space in which your website will live (host) and give it a unique address (domain). I recommend SiteGround* as your WordPress host. They have affordable rates, quick speeds and awesome customer service. Your domain will cost you about $10 a year. Hosting will cost an average of $150 a year.
Check out my tutorial on how to set up your domain and hosting with SiteGround.