Martin herself also showed off the new tattoo in an video she posted to her Instagram story on Sunday. In the clip, she and Carter appear to be eating at a restaurant when Martin reaches up to brush Carter's hair back, revealing her name penned above his eye.
For his part, Carter hasn't shown off the tattoo to his own Instagram followers.
When Carter posted a pic from the hair coloring session, he shared a pic that only showed the left side of his face in profile, hiding the body art.
It's hard to tell when Carter got Martin's name tattooed on his face, but he doesn't appear to have the ink in Instagram photos snapped by both himself and Martin in late February.
Meanwhile, Carter seems to be in good spirits. The 32-year-old posted a snapshot of himself sitting on a dilapidated couch in the middle of an empty field on Saturday, while drinking a bottle of beer. The new tattoo is visible above his eye in the pic.
"So far 2020 has been great to me," Carter wrote. "Lots of cool things coming up looking forward to getting back to work after some much needed time off."
Carter previously surprised fans last year when he first revealed the sizable face tattoo he'd gotten on his left cheek.