Caleo
Is there supposed to be a connection between Shakespeare's son and Hamlet Prince of Denmark?
At the start of the film there were captions saying that the names were interchangeable. I don't know how 'factual' that is, but obviously the setting is before the first dictionary and few could read or write their name, so it's not beyond the realms of possibility.
It doesn't matter, really - it's more that in the story of the book and the film, he was working through his feelings about his son, his family, his place in the world as he wrote. I think that is 100% believable, although it is impossible to know whether it is 'factually' true.