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Vanities is the name of a series (1923-1940) of musical revues by Earl Carroll, a 1976 play by Jack Heifner, and a 2000's musical adaptation of the latter.
The Bock and Harnick musicals Tenderloin and She Loves Me have unrelated songs titled "Dear Friend."
No, Titanic: The Musical is not based on the film, in fact it predates it.
Of course, as the Titanic was an actual ship, there are many books, paintings, etc. titled after it.
ACT is the acronym for both the American Conservatory Theatre in San Francisco, and A Contemporary Theatre in Seattle. Ironically, both do annual holiday plays of A Christmas Carol.
In Italy, France and Germany, opera houses tend to have similar names. Some examples include:
Teatro Regio: where is it, Turin or Parma?
Stadttheater: found, among other places, in Magdeburg, Dresden and Munich. Hardly an amazing coincidence, since it's German for "City Theatre" and is usually followed by the name of the specific city unless it's clear from context which one is meant (if you're in Munich talking about the City Theatre, most people are going to naturally assume you mean the one that's also in Munich and not the one in, say, Geneva).
Various theaters in Paris have the same name.
In Commedia dell'Arte, characters are usually named after a specific stock character they are portraying, which is why so many characters from the different plays of this genre carry the same name.
Shakespeare has four plays (Twelfth Night,The Merchant of Venice,The Tempest, and Much Ado About Nothing) with major characters named Antonio. Two of them (in Twelfth Night and The Tempest) are paired up with Sebastians, and at least two of them (Twelfth Night and The Merchant of Venice) are arguably gay.