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Calvin's last name has never been given, and neither has any of his parent's names. This was actually why his uncle Max only showed up for a brief storyline; the creator of the comic, Bill Watterson, ultimately felt that while it was fine to have him as someone for his parents to talk to, it felt far too awkward to never have Max refer to them by name and he never made a return appearance.

The general tone of the comic is fairly light-hearted, with a big emphasis on goofy slapstick comedy contrasted by clever wordplay and often surprising adult-centered jokes that'll hit you like a slap. A big part of the comedy is, as Watterson put it (paraphrased) "It's really funny to me when people express deeply stupid ideas with really fancy terminology." One notable example you might have seen is that one bit where Calvin asks his mom for money to buy a Satan-worshiping rock album and his mom replies that there's nothing genuine about them and they're just putting on the attitude for shock value, and comisserates with Calvin as he deplores that mainstream nihilism can't be trusted. He concludes that childhood is disillusioning.

There is a LOT of criticism of the extreme materialism and selfish mentality of the late 80s, when the comic was initially written. This may go a long way to explain how its aged so well; much of what it criticizes resonates well with people today.

Bill Watterson views comic strips a legitimate form of artwork, and repeatedly fought to have more space to draw more beautiful and artistic backgrounds, which was a very hard fight and unpopular even with other comic strip artists. He eventually did win some compromises and a lot of Calvin And Hobbes' artwork shows it, with the use of space to indicate time as well as a sharp contrast between the often plain environments of mundane life contrasted by the wildly beautiful imagery of Calvin's imagination (which often sports realistic depictions in an art shift of sorts).

Hobbes is explicitly not an imaginary friend, by word of Watterson himself. We don't know WHAT he is exactly, and Hobbes is apparently unaware of the strange nature of his reality; people look at him and only see an ordinary stuffed tiger plushie, but he has a tangible effect on the world that would be physically impossible for Calvin to do on his own. He's apparently been around for a while, and was apparently around when Calvin was a young baby.

On that note; Hobbes has implicitly killed (notably treated as both a gag and also with the vibe of 'he's a tiger, duh') and while he doesn't do it again on-screen, he doesn't have any moral issues about it. Calvin claims that he's never had trouble bringing Hobbes to school because the last time he did, Hobbes killed and ate a bully named Tommy Chestnut and simply comments that it was gross and he needed a bath. Calvin's tried to repeat this again, but Hobbes was grossed out at the thought having to eat a kid raw and not being allowed to use an oven first, or complaining that children are too fattening.