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.