Hamnet

[GreatGazoo]

3. That's what I mean

The Hamlet = Hamnet thing was made up for the fictional book and movie. In primary source documents from the era Thomas Nashe is writing about the play Hamlet in 1589 and says that he saw it two years earlier eg. 1587. Philip Henslowe hosted performances in 1594:

This important source, Wits Miserie and the Worlds Madnesse (1596), contains a well-known reference to a play about Hamlet... The earliest reference is found in Thomas Nash’s (or Nashe's) famous preface to Robert Greene’s Menaphon (1589)...

theatrical entrepreneur, Philip Henslowe (1555/6–1616). In his book of accounts and memoranda (now held at Dulwich College), Henslowe says that a play called Hamlet was performed by his company at Newington Butts in June 1594.

https://www.bl.uk/collection-items/reference-to-early-hamlet-play-in-lodges-wits-misery-1596