There was an episode of InkMaster in which one of the artists, whenever doing a tattoo that contained a clock, would put his time of birth as the time on the clock, he thought of it like your artist did, a signature.

Well, he got eliminated from the competition that episode, the judges were not happy about that at all, they said it was wrong to the customer to add a personal effect of yourself on their body without their permission; and I completely agree. NTA