When a guy tattoos your name, it is an outward expression of his love and devotion to you. It could mean a variety of things, depending on the context. It could be a symbol of his commitment and how proud he is of your relationship, or a reminder to himself of how much he values you. It could also be a show of affection, a way to tell the world he loves you, or a way to keep your memory close to him always. Whatever the reason, it is an extremely romantic gesture and likely has a great amount of significance for him.