Thanks for your message! ROUND is certainly a Dudley name and I am sure if we go back far enough, we'd find that all ROUNDs there are related somehow.
I have a James Arthur ROUND so of Isaac ROUND in my family tree. He was aged 3 on the 1861 census, so would be about the right age for your James. However there would have been hundreds of James Rounds in Dudley at the time, so the first step would be for you to obtain the marriage certificate for James and Jane Moy. This will give James' father's name. If by any chance it is Isaac then we could well be related!
Do let me know if you find anything else out, or need a hand with research :-)