digital tattoo
n. The difficult-to-remove digital imprint that a person creates by posting information online and by accessing online resources.
Examples
2013
Giving a child any device with an Internet connection requires oversight. A sudden wave of adolescent emotion could generate a photo or a social media message that could become what Gail Lovely, a former teacher and owner of Lovely Learning, a consulting firm for schools, refers to as a "digital tattoo" that comes up in a job interview 10 years later.
—Warren Buckleitner, “A Digital Back-to-School Checklist,” The New York Times, August 28, 2013
2013
The knowledge that messages will vanish also frees users from what Cornell Professor Jeff Hancock calls the "digital tattoo." "If you do something online, it's difficult to remove," he said.
—Katharine Schwab, “Snapchat takes digital retro: free to be candid,” The San Francisco Chronicle, August 11, 2013
1999 (earliest)
Yet the dispute underscores an issue that is becoming more prominent as a growing number of digital devices use a plethora of identification numbers to communicate with each other effectively and securely.

"My problem is that it happens without the user knowing," said Bruce Schneier, an encryption expert and industry consultant. "It's the slow erosion of privacy on the Net without informed consent."

Jason Catlett, president of Junkbusters, a consumer privacy organization, called the ID numbers a "digital tattoo."
—Miguel Helft, “Fingerprints on your Office files,” San Jose Mercury News (California), March 09, 1999