You could write essays on this. In fact, people have! Other names include Miranda, which Shakespeare coined, and which is supposed to have a connotation with wondering or admiring - and Miranda wonders at everything around her, and provokes wonder wherever she goes. Ariel is airy, Caliban connotes "Cannibal," it goes on. Juliet is so named because she was born in July (the Nurse mentions it), and it also suggests a precocious nature; Falstaff is not to be relied on, etc....
In Romeo and Juliet two of the characters names reflected their personalities. Benvolio was a kind and benevolent character while Mercutio had a mercurial and fiery nature.
Tybalt shares the name of the prince of cats in the Reynard The Fox stories, and Mercutio mocks him for this throughout the story. Like most cats, Tybalt is rather pissy and aggressive, and like this specific other Tybalt he's also argumentative but easily outwitted.
Lucy The Slut in Avenue Q (a video screen at one point shows that her name is actually Slut, Lucy The).
Rod. In a comic sense, he plays the straight man in the scenes with his roommate Nicky, and in the technical sense his puppet is constructed with a single control rod. Also subverted, however, in that despite all the "straight" connotations to his name, he is in fact secretly gay.
Emily: Weird name. Prior Walter. Like, "The Walter before this one." Louis: Lots of Walters before this one. Prior is an old, old family name in an old, old family.
This is especially relevant as Prior later meets the ghosts of two of his ancestors who share his name.
The long-forgotten musical The Stepping Stones, the principal female character was Rougette Hood, whom everyone called Little Red Riding Hood (naturally). The villain was named Otto De Wolfe, and his associates were named Remus and Lupina.
Urinetown doesn't get really specific, but The Hero's name is Bobby Strong and the female ingenue's is Hope Cladwell.
Not to mention her father, rich businessman Caldwell B. Cladwell ("Caldwell is well-dressed"), whose wealth and style contrast with the miserable poor he keeps in virtual financial slavery, and the money-grubbing-by-necessity Penelope "Penny" Pennywise.
A character in Andrew Lloyd Webber's Phantom of the Opera is surnamed 'Piangi' (tears).
Waiting for Godot: Not sure about Vladimir and Pozzo, but Estragon is French for "parsley"—as in a garnish without substance that makes things look nice. Lucky, on the other hand, is decidedly not lucky.
In the musical Chicago, the only two innocent characters in have names that imply that they are fools:
Hunyak, the only wrongly convicted prisoner, and the only one to be executed. "Honyock" is an ethnic slur that was popular in America from the 1880s through the 1950s. It is derived from a Hungarian word meaning (among other things) "simple minded" and "loser." Mostly directed at Central-Eastern Europeans.
Amos, whom Billy calls "Andy" when he steps down from the witness stand. This is a reference to Amos 'n' Andy, a race comedy radio series originating from Chicago radio station WMAQ beginning in 1928. Most of the series' male characters were performed by two white comedians who had worked in minstrel shows on vaudeville. In the series, Amos was a schemer and Andy was innocent and a bit simpleminded. (This is a happy accident as the name Amos is a carryover from the original play and silent movie which both predated Amos 'n' Andy.)
A short play titled "The Play Called Noah's Flood" centers around a tiny medieval village trying to put on a morality play as part of a competition with neighboring towns. Many of the characters' names are appropriate for the characters they play, particularly those representing the Seven Deadly Sins: Hester Mountamous plays Gluttony, Laggard Slog is Sloth, Lascivia Sly represents Lust, Yerna Covetine is Envy, and so on.
A very stealthy example in The Addams Family musical: Wednesday's allegedly normal fiance, who causes her to feel unwelcome emotions like happiness and love, is named Lucas- which derives from the Latin word for "light." Less pointed examples are his parents' names: Mal ("bad," the strict, conservative, workaholic father) and Alice ("noble," the put-upon but accepting and supporting mother).
In The Duchess Of Malfi, the husband of the Cardinal's mistress is an old lord named Castuccio, Italian for castrated, or impotent.
In Dorothy L. Sayers's The Emperor Constantine, Flavius tells Helena that he named his youngest daughter Anastasia, after the Christian belief that in the resurrection there would be no marriages — and therefore no political divorces.
In Johann Wolfgang von Goethe's Faust II, there are three strongmen (sent by Mephistopheles, so probably demons) named Raufebold ("ruffian"; he's a young Blood Knight), Habebald ("will have soon"; medium-aged, he wants to make booty in the war more than fight) and Haltefest ("hold tight"; he's old and prefers to keep what he has). And the sutler woman Eilebeute ("hurry for the booty"). Then again, their names aren't used in the dialogue.
Magda from Tanz der Vampire is the maid at the inn, and her full name is Magdalein. "Mägdelein" is the German word for "servant".