While it is super much fun to imagine a Hamlet running around the kingdom in his birthday suit, it’s likely that the nakedness is more a reflection of vulnerability than actual nudity.
An actual nude Hamlet would suggest the antic Hamlet, the Hamlet who is still playing the crazy card – but a metaphorically naked Hamlet is likely without his usual princely protections.
I suspect that this also suggests that he is alone and therefore without any of Claudius’ spies. If the ruse is that Rosencrantz and Guildenstern were protecting him on his trip to England, to be returned naked is to suggest that he’s returned without anyone controlling him or reporting on him.
Nakedness can also suggest a brand new start – a rebirth – a beginning again.