You do. You always want to maintain control of your own domain.
You are considered a registrant when it comes to purchasing and renewing the domain you want. If this is your first time, you purchase a domain name from a registrar (i.e. Name.com, Godaddy, Domain.com, Network Solutions, etc.).
These companies are middlemen. So when you buy a domain from a registrar, like Godaddy, they verify that the domain meets certain requirements and then they submit the domain name and your information to the appropriate registry operator. Registry operators maintain the master database for top level domains (.com, .net, .us .xyz, .site, .club, etc.).
All this to say, you have to purchase your domain from a registrar and pay a yearly fee for it (typically 1-10 years at a time). It will always belong to you if you keep your registration up to date. If you let your domain expire, the consequences are up to your registrar and the terms of service you have agreed to. Think of it like a yearly insurance policy. Do not let it expire.
Pro tip: Always select the option to auto renew your domain and keep your payment information up to date.
If you want to know who is listed as the owner of a website (registrant), who it was registered through (registrar), or when it expires you can search the domain name from either the ICANN or WHOIS websites. You can also pay an extra fee to your registrar to have this information private and not show up on the search results.
I didn't purchase my domain, a different company did.
If you didn't initially purchase your domain, you need to contact the company that did and get your registrar login info. I hope you're still on good terms with them because it is very important that you have this information. You need to take control of your domain name.