Tattoos on Covert Operatives

If you're a spy, a criminal, a terrorist or anyone who needs to remain unidentifiable: does it make any sense to have any/lots of tattoos? Any time I see movies (from the modern era) that depict super criminals and terrorists as being tattooed or otherwise exceptional/memorable, It just makes me shake my head. I mean, how super (i.e. "successful") can you be in a covert operations field if you're easily identifiable? It feels like identifiability is inversely-proportional to ability to be covert.