Heather W. answered 06/30/19
Literature instructor, specializing in Shakespeare
I give this answer with the clarification that my area of knowledge is Shakespeare and not so much Greek mythology! I would think we associate the name with the Shakespearean figure more so than the Greek figure, but the former is my area of study (so I'm bias).
Though he wasn't formally educated at a university (Shakespeare's formal education stopped when he was around 13 because of financial limitations), Shakespeare probably did have a knowledge of Greek mythology (many names in Shakespearean plays have Greek roots and his tragedies have similar themes to Aristotle's model of tragedy).
In The Odyssey, Laertes in Odysseus's ailing father (he remains in Ithaca on a farm -- he is in failing health and is heartbroken). Laertes is given aid from Athena, helping Odysseus kill the father of Antinous's. Laertes, in Hamlet, is the son of Polonius and the elder brother of Ophelia. I don't think it would be crazy to make a connection between the two men.
Both men are heartbroken -- The Odyssey's Laertes over the apparent loss of his son (he won't even go to Odysseus's home while Odysseus is away) and Hamlet's Laertes over the loss of his father and sister. Both men want what has been taken away from them (a loved one) back again and they both want revenge. Both men are wronged by those with greater power then themselves. In The Odyssey, Laertes is kept away from his son because of the war and subsequent journey home (the gods and goddesses play a hand in the journey home for Odysseus that last for so long). In Hamlet, Laertes' father (Polonius) is killed by Hamlet (Hamlet thinks he's killing Claudius) and Ophelia dies from an apparent drowning (Did Hamlet drive her to her death by taking away his love and attentions? Could Gertrude has stoped it? Did the death of her father drive her to her death?-- Regardless, Ophelia seems to be a result of the selfish actions of the royal house).