Let me turn this back around--what significance do *you* see in the name? If none, move on and focus on something else. If some, what and why?
Try this on: Homer's Laertes is the father of "the great tactician," the Greek warrior most known for his intelligence. Shakespeare's Laertes is the son of the biggest doofus in Denmark. What does THAT mean? Maybe it's just a lit joke--Shakespeare wasn't the first, and certainly not the last author to throw in a reference for fun. Maybe the juxtaposition of intelligence is a comment on how times have changed for the worse--something like: "in the old days, Laertes was connected to the smartest people around, but now, look at this Laertes...the kids today, I tell ya." Or maybe it's a subtle hint that Polonius isn't as dumb as he looks...this is a reading of the play that I've heard from some scholars, that Polonius is a puppet master who's just playing dumb, and while I don't buy it myself, that doesn't mean it's without merit, and his son's name could be a little piece of circumstantial evidence for that interpretation.
Or try this: Homer's Laertes is mainly associated with grief. By the time we meet him, he hasn't seen his son in 10 years and has all but given him up for dead. Compare that to Shakespeare's Laertes who gets into a kind of grief olympics with Hamlet at Ophelia's funeral. Maybe his name is a way to foreshadow that grief lies ahead. There's also some irony there, since Homer's Laertes' grief ends when Odysseus comes home, but Shakespeare's Laertes loses everyone for real and then dies miserable himself.
There are probably other possibilities.These questions generally don't have absolute answers. Even if we had Shakespeare's diary and it had an entry that said something like: "I was reading o'er Homer yesternight and bethought what a jest 'twould be if I did name the fool's son after the tactician's father in my new playe," it still wouldn't mean that that was the only valid interpretation.
I'd be happy to help you explore Shakespeare or any other literary work any time!