Looking at things like this - https://phys.org/news/2013-03-easy-identity-cell.html
https://33bits.wordpress.com/about/
etc
Having DNA and just looking at the traits that person has will reduce the population down to a pretty manageable number. Any other bits - location, gender, etc will be enough to make an educated guess to an almost certain one. This will not become more difficult to do in the future.
[1] http://www.pnas.org/content/early/2017/08/29/1711125114
[2] https://www.technologyreview.com/s/608813/does-your-genome-p...
I used 23andme years ago, using a fake name on the website and a kit ordered by someone else (a friend ordered kits). I should see if I can use their GDPR process to purge it before any relatives give it a shot and start a scandal about the presence of John Doe in the family tree.
[0] https://globalnews.ca/news/4171752/golden-state-killer-dna-g...
Right now, it's the wild west.