The main hint hides in line 53, Threnos. It's a rare word, and a perfect anagram of shorten, or thrones. Shorten explains why the poem shifts from four lines to three lines. Three is a one-way anagram of Threne in line 49, and Threne is a one-way anagram of Threnos in line 53. Purpose of this three-threne-threnos wordplay tells readers, that this poem can be solved by anagrams.
Twelfth Night is the end of a festival. The full title, "Twelfth Night, Or what you will" tells the world, "End joy, or do what you will." The naming is focus on the puritan steward Malvolio being ridiculed by the mal-folio MOAI.
The Tempest is first play of the First Folio. Ship-master and Boteswain are the first two characters on the stage. The beginning of the First Folio works like a preface to all Shakespeare’s plays
Philip Sidney created one-way anagram in his Song for an Accession Day Tilt (1577). In the song, Philisides and Mira can be easily transformed to Philip Sidney and Mary.
Since the name on a book's cover isn't always the writer of that book, e.g. Martin Marprelate, Shakespeare wrote Shakespeare can't be deductive.
Wilton House poets play with names. Robert Greene called himself Roberto in Greene's Groat's-Worth of Wit. Roberto's brother is named Lucanio; their father Gorinius.
Enter Camillo and Archidamus.Archidamus is the name of some Sparta kings.
Archidamus appears only in the beginning of The Winter's Tale.
No one calls the name; no audience will hear the name.