Yes, this is either a scam to get you to pay some "processing fee" or deductible or plain vanilla insurance fraud. Why in the world you need your DNA tested anyway? As far as knowing your info, that can happen in many ways. Insurance company leak is possible. If you are older, over 55, you are targeted since you are apt to be trusting, and also can be intimidated.
Do NOT call these crooks back. Do not talk to them if they call again. That just gets you more calls from them and others. Block the calls from that number.
You might be able to report this to your insurance carrier. It is worth calling your carrier to see if they are interested in having the phone number and the name the crooks are using. Long shot, but might help others.
Many calls and usually I don't pick up. Last two times, I did pick up and they have a convincing story asking for my son and referring to the pain cream he is approved for and just need to know the cause of the pain. I told the woman that I would have to check and call her back. She actually gave me a number that of course, had a voice mail box that was full. Second time, it was for a cream that another female claimed was probably for eczema or something like that. She knew his name and age but avoided answering other questions. Not good!