Nickname isn't technically inaccurate, but the more appropriate word is pseudonym; if you're participating in an underground rebellion against your government, that's maybe not the kind of thing you want your real name attached to. So you make up a fake name for all of the illegal activity you're getting involved with and interacting with the other people in your conspiracy in an effort to keep the police from attaching you to any of it. After all, Vladimir Ulyanov never did any of those horrible things, it was all that terrible man N. Lenin!

As for your curiousity about the origin of those names, Lenin is generally assumed to be derived from the river Lena in Siberia. I've read it was common for fake names to be derived from natural sources such as rivers, and that Lenin was trying to make fun of his compatriots who frequently called themselves Volgin (after the river Volga). Although another story I've read, with equally little to back it up, is that it happened to be the name of a dead man whose passport Lenin used when he fled the country (although as I recall he had been using the name for at least a year before the man died).

Molotov's alias, as you've already noted, comes from the word for hammer, he was trying for a name that would be immediately associated with industry and the proletariat.

Trotsky's name, according to legend, comes from the name of a guard (or the warden) of a prison he was sentenced to. According to one story I've read, they had many conversations in which the man gave him solid advice about leadership, and when he chose his fake name he chose to honor the man he felt had taught him valuable lessons.