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.
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Gillian
"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!"