Uranus (Ouranous, in the Greek spelling) was a sky god, who along with Gaia (or Gaea, or whatever spelling you'd rather) created life. If you think about it, it's pretty logical that an even-more distant planet would be named after him; he was, yes, the father of Chronos/Saturn. He imprisoned some of Gaia's children for being monstrous freaks, so she armed Chronos/Saturn with an obsidian sickle. He went after his father with it (castrated him with it, in some versions!) and took over his place as head god. Ouranous/Uranus fled beyond Chronos/Saturn's reach . . . or orbit, as it happens.
As for Neptune, I don't remember. I believe Isaac Asimov covers it in Words from the Myths, but again, I don't know what happened to my copy.
"Now everyone was giving her that kind of look UFOlogists get when they suddenly say, 'Hey, if you shade your eyes you can see it is just a flock of geese after all.'"
"You can't erase icing."
"I can't believe it doesn't work! I found it on the internet, man!"