A rare example for Cirque du Soleil, in Amaluna, Romeo exclaims "MIRANDA!" when the Black Peacock Goddess flies off with her just before the Chinese pole act; Miranda likewise shouts "ROMEO!" when Cali pulls him below stage at the end of the tightrope act.
The adults exclaim Sisi's name at various points to get her attention, particularly when she's walking the rope. The Takarazuka Revue production has Ludovika calling Sisi when she catches her daughter reading poetry.
Sisi herself exclaims "Papa!" when she spots Max.
"Eliiiiiiisabeeeeeeeth...": When either Franz Joseph or Death is trying to charm/coax their way into Sisi's good graces.
"Elisabeth, Elisabeth!": Sung by the chorus of the dead.
Japanese productions: Franz Joseph snaps "Rudolf!" at the Crown Prince when chastising him.
Fiddler on the Roof: Fruma Sarah's screeching during Tevye's Dream. "TEEEEEEEEVYE!"
In Hamilton, most of the characters have a leitmotif that goes with their name that generally introduces them from scene to scene, which is necessary with the double casting. For example, "Take a Break" is the first time Eliza and Angelica appear in the second act, and within the story, they've been apart for some time. They both greet each other with the same tune they introduced themselves in the first act "the Schuyler Sisters".
Eliza: ANGELICAAA! Angelica: ELIIIIZA! Alexander: The Schuyler sisters. Angelica: Alexander!
Everyone, from Eliza to Washington to Burr to Hamilton himself, has a moment where they shout/sing/cry Hamilton's name.
Also, "Aaron Burr, sir!"
Everyone - except Lady Bracknell - does it at the end of Oscar Wilde's The Importance of Being Earnest. Names do play a very important part in the play. Earnest! What a name!
Edward: Then, from my lips/Came a voice, came a name/ I cried "Jane" from the depths/ I called out/I cried "Jane"
In Memphis, at the start of Act Two when Huey gets his own TV show in the song "Crazy Little Huey", both Huey and some dancers from the show proceed to sing "Hueeey!" Huey himself singing "the name is Hueeey!" a few times before the final "crazy little Huey is on your TV!"
In The Merchant of Venice by Shakespeare, Shylock says his daughter Jessica's name a lot in their first scene. One gets the feeling he likes her a lot, but he's somewhat overprotective and possessive. "What, Jessica!" — "What, Jessica!" — "Why, Jessica, I say!" — "Jessica, my girl." — "Hear you me, Jessica."
Miss Saigon: KIIIM! Happens during the fall of Saigon scene and at the end. If the actor playing Chris is feeling particularly hammy, he may add a Big "NO!".
The Phantom of the Opera and Raoul loves to sing "CHRISTINE" loudly and Christine herself loves saying "RAOOOUL" loudly.
In Pokémon Live!, Team Rocket asks the audience to yell "Team Rocket" loudly.
In Ragtime, Father does this to his son during the final lines of "What a Game", when said son won't stop repeating the other baseball fans' less-than-polite language.
Ensemble: Whaaaat a... Edgar: Up your alley! Father: EDGAR!!! Ensemble: ...gaaaaaaaaaame!
Rebecca: The title character never appears, but Maxim, the narrator, and Mrs. Danvers all say her name frequently. Mrs. Danvers even has a song (which gets three reprises) called simply "Rebecca".
Older Than Steam: In Shakespeare'sRomeo and Juliet, Juliet Capulet begins a monologue on the meaning and importance of names with the repetition of her crush's name: "O Romeo, Romeo! Wherefore art thou Romeo?"
When Wendla's mother in Spring Awakening drags her off to get a back-alley abortion, Wendla is confused and terrified, screaming "MAAMMAAA!" as she is dragged off.
Then in Act II, Tony gets news of Maria's betrothed, Chino shooting her out of jealousy for Tony, causing him to run out yelling, "Chino! Chino! Come and get me too, Chino!"