Earlier quoted context omitted.
Given the nature of the service, you should probably treat it as inherently pseudonymous. You're handing over irrevocable genetic data which will link you to relatives. Whatever their data protection assurances are, you have to imagine the worst case scenario - massive data leakage. And if this happens then you will in all likelihood be identifiable.
Obviously I don't trust any assurances, but on the other hand I'm handing over my genetic data all the time because parts of me end up over in the hands of 3rd parties whenever I go outside but they just happen not to run test on those. If I can have a test that is not connected to my persona, from their perspective the data would be as valuable as running a test on the hair in the barbershop or picking a random left…
If you're worried about getting arrested for one of the many crimes you've committed, and you want to meet far-flung relatives, you're kind of in a bind here. Assuming unlimited cooperation between the police and the DNA/ancestry services -- which your threat model in this case would require -- even if they don't have your name or address, they could fabricate a half-sibling/double-cousin in the system and have them reach out to you. What, are you not going to talk to and eventually meet the cop pretending to be your previously unknown half-sibling/double-cousin?