For Ricean vampires (idk the rules with others), I don’t think dye would last forever bc they can cut their hair, and the dye would be effectively removed. 

Dye is a color treatment on material that’s basically dead and outside their bodies. Even though their hair does not grow longer than the length it was when they were turned, it can be cut off and will grow back their natural color. I don’t think the dye would vanish during turning, either, like nailpolish wouldn’t vanish during turning. The nail underneath would change to that vampiry glassiness, but not be visible. The hair would change in texture inside the dye.

With something like a tattoo, I would think that it could be permanent, if the mortal had them before being turned, because the ink is under the skin, but maybe the vampiric parasite would reject the ink as being unnecessary. I don’t think we have any tattooed vampires in canon to know for sure.

@thebibliosphere? Thoughts?