The worry that stops more people from testing than cost ever does, answered directly.
Legally, in most cases you do, but what a company can do with your data depends on the consent you signed, so the privacy policy matters more than most people realise.
A reputable provider does not sell your data or share results with insurers, employers, or relatives without your explicit consent, but protections vary by company and country, so check the specific policy.
Owning your data means being able to remove it. Look for a provider that lets you delete your data and destroy your sample on request, and that is transparent about any limited records it is legally required to keep. If a company makes deletion hard to find or hard to do, treat that as a warning sign.