Most roofing companies find out who owns their website on the day they want to change supplier. It is a bad day to find out, and it is entirely avoidable, because every part of it can be checked this afternoon while nobody is arguing.
Four separate things can each be held by somebody else. They are usually held by different people, which is why the answer is never simply yes or no.
1. The domain name
The address itself. This is the important one, because it is the thing printed on your van and typed by your customers, and it is the one asset that genuinely cannot be replaced without cost.
It should be registered in your business name, with your email as the contact, in an account you can log into. Somebody else can manage it for you, which is normal and fine, but managing is not owning.
How to check: search for a whois lookup and put your domain in. Many registrations hide the owner's details for privacy, which is normal, so if it comes back private the real check is different: can you log in to the registrar account yourself? If you cannot, and you do not know who can, that is your answer.
2. The hosting
Where the site actually runs. Less critical than the domain, because a site can be moved, but you want to know the answer.
How to check: ask your supplier where it is hosted and whether the account is in your name. On an all-in-one platform, hosting and the site are the same account, which makes this the same question as the next one.
3. The site itself
Two parts, and a contract can treat them differently. The content, meaning your photographs and the words about your business, is normally yours, though it is worth putting in writing if the supplier wrote the copy. The design is frequently licensed to you rather than sold, especially on a monthly deal.
Neither is a problem as long as you know which one you have. It only becomes a problem when you assumed you owned something you were renting.