Why does my son's name come up on my icloud messages when I use my mac to send one?
More info would be helpful. 

But assuming you are using the messages.app that comes with macOS. 

Open messages, go to the messages menu and select preferences > Accounts.

It is likely that the account that messages is using is your son's. You can uncheck his account (or just delete it) and add yours. And by "yours" I mean the same account you use on your iPhone/iPad which is usually the email address associated with your AppleID.