Yes, with determined sleuthing. You can try, but there are no guarantees you'll be able to figure it out. Your first step would be to look in the History, by clicking the "history" tab near the top of the page at hand. At this point, you'll get a lot of usernames like "Ged UK," "Juliancolton," "RockMFR," etc. Some of those look like real names but there's no guarantee that they're the user's real names.
For some pages you'll also get IP addresses, like 255.254.253.252, 184.108.40.206, etc. You can look them up in WHOIS, but that might not tell you anything more specific than "Comcast in Houston" or "AT & T in Seattle." Seigenthaler's slanderer was tracked down to a delivery company in Nashville, but if Brian Chase hadn't stepped forward to confess, we still wouldn't know his identity.
When you have a username, you can go to their user page and learn a little something about the particular user. But they don't have to put down the truth. There was a famous user who said he had a doctorate in theology and a doctorate in canon law. He was exposed as a fraud, but to this day there are several Wikipedia users who claim to be medical doctors, rocket scientists, lawyers, etc., and it's not easy to verify their credentials.
Good luck in your sleuthing.