Yes, it is very stupid. It's stupid even if you marry them. You never know what life is going to throw at you. You may break up or divorce, and they'll never be involved with you again, and then you'll just have a constant reminder etched in your skin of that person and a permanent reminder of why you split up.
Take Johnny Depp for instance. When he was engaged to Winona Ryder, he had her name tattooed on his arm (Winona Forever). After they split, he had to spend the extra money (even though he as an actor can afford that kind of work, but that's not the point) to get it fixed to say "Wino Forever". Now he gets asked about the tattoo by fans and interviewers, and even with the edit, it probably brings up memories of Winona he would prefer not to think about often.
That's all a tattoo is. A permanent reminder. And if not a reminder, it's still permanent, and you may decide you hate it one day, and then not have the funds to have it removed. Tattoos are a huge decision, period, and should be VERY carefully thought out before any decisions are made about getting one.