So similar to Hamnet, the name of Shakespeare’s dead son, fraternal twin to daughter Judith. Hamnet died in August of 1596; Hamlet was written at some point between 1599 and 1602. It might be neat (and by that I mean “well-composed” and “skilled and precise,” as opposed to, like, “really cool”) to think that Hamnet’s death and the birth of Hamlet might be related, but it’s probably not the case, and such critical opinion has fallen out of vogue. The connection to Twelfth Night is probably more probable.
But worth a mention, all the same.