Was Hamlet a real person?

No, Prince Hamlet was not a real person.
However, the story of Hamlet, although mostly known from Shakespeare’s eponyomus tragedy, has been around for centuries.
It is based on the Scandinavian legend of Amleth, and although there are many different versions of the story, the one that is widely known and most often compared to Shakespeare’s retelling is that of chronicler Saxo Grammaticus from the thirteenth century. This version talks about Amleth, the rightful heir to the throne of Jutland, who has decided to avenge the death of his father, Horwendil, by killing his uncle Fengo.
And similarly to Hamlet, Amleth feigns madness to hide his true intentions, kills an unnamed eavesdropper (as Hamlet did Polonius), and finally succeeds in avenging his father by murdering Fengo.