I believe this was also Shakespeare's son's name, but tragically, he passed away at a pretty young age. I wonder if the
Hamlet similarity made the name less popular? I mean,
Hamlet isn't necessarily the happiest of stories. Or perhaps it's the ham + net thing that just makes it hard to use!
I don't think the "ham" itself is off-putting, as
Hamilton is still usable, and I think
Hamlet would be a cute middle name choice.