At Chicago Tattoo & Piercing Co., which has been in business in that city since 1973, the employees have a name for tattoos on the hands, neck and face. “We call them job stoppers,” said Joel Jose Molina, a tattoo artist at the shop. “Your possibilities are cut down. You’re going to be working at the Trader Joe’s putting groceries away or working that bar job.”

Or then again, you might be cutting platinum albums and performing at this year’s Lollapalooza Festival, like Post Malone. Or broadcasting your amazing pop star life to your 101 million Instagram followers, like Justin Bieber.

Both musicians have tattoos on their faces, a once taboo area to ink.

Post Malone has “Stay Away” in curly script on his forehead and the words “Always” and “Tired” below each eye, while Mr. Bieber has a tiny, under-eye cross.