There's a simple anonymity hack, unless of course your relatives "out" you. I bought my 23andme kit from Amazon, then registered on 23andme website with a fake name. I have my results, but as far as 23andme are concerned I'm John Smith.
How recently did you do this, and was there any information collection like that?
And does the kit have any sort of identifier with it? If so, I was considering some sort of 23andme kit remixing service, where people pool funds to buy a bunch of kits, and then randomly select a kit from the shipment. :-)