This scene is often cut. In Backwards and Forwards, David Ball explains why this is a mistake. While it’s true that no real action happens here, in it we see Polonius at his most devious, setting up a spy to get information about his son.
It’s important because its gives us insight into a character we might otherwise see as a sweet old man killed by our hero. I think that’s smart.
This is the first line in the first scene in the Act 2 and here we meet Reynaldo, who we will never see again and whose name shows up nowhere else in Shakespeare. It’s not a generic name. It seems important somehow.
Polonius will say it more than once.
He does not send Servant or Messenger to go seek out gossip about his son. He sends a character with a name and a unique one at that.
I have questions about Reynaldo. First, what sort of name is that? It’s not Italian. There is no Y in Italian but it sounds Italian. Perhaps it’s Spanish?
But again, I wonder: What are all these Latin folks doing in Elsinore?
Why is almost everyone in service Italian or Spanish or Portuguese? Time to go searching dissertations again. There must be one called The Latin Influence in Hamlet: An Historical Context of The Latin Presence in Shakespeare’s England and Denmark, too.