Short answer
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.
When you order a test you typically sign two things: consent for the test, and consent for what happens to your data afterwards. The second one is the one to read carefully. Responsible providers let you opt out of research use, download your raw data, and delete your account and sample. Before testing with anyone, read how they store data, who can access it, and whether you can have it destroyed.