This is interesting when you dig into the etymology of these words. Whereas pseudonym comes from "false", anonym comes from "lacking, not having", shading the meaning away from "fake name" to "nameless". If you search around, one synonym you'll see is nom de guerre. Knowing the "guerre" part had to be war, I find this a bit strange: "war name"? And then why not "nom de plume" for a synonym? Justing musing this morning.... :0)