That’s why I bought the tests on Amazon on Father’s Day sale. Then used completely fake info and fake email to register on the testing company site. Totally anonymous as there’s no way to link the purchase to results.
Eventually that data will become associated with your real identities. How could it not? you're obviously so-and-so's grandfather/first-cousin/whatever, and they gave their names.
For 23AndMe you can buy the kit in cash in a store like Target and post the sample. Then use anonymous connection and email to use the website and get the results.