I was wondering the other day what would be the legal implications if (G-d forbid), one got a tattoo of the Sacred Name of G-d on his skin. It could obviously never be lasered off, but could one even expose it in a bathroom? How would someone take a shower or a bath? It has very interesting implications, no? Secondly, what would happen if someone wrote the Name on their skin in pen? I suppose one couldn’t bathe until it had completely faded.
The question of G-d’s name written in ink on the skin is addressed in Masechet Shabbat 120b and Hilchot Yesodei Hatorah 6 6. The name must be covered when the person is in the bathroom or when he is undressed. He is allowed to bathe with it covered (Shu”t Noda B’Yehuda II Orach Chayyim 17 permits this only if the immersion is a mitzva) even though the water will, on its own, erase the name, but he is not allowed actively to erase it.