I don't know why they didn't add this the first time but they didn't. So here we go again. Yes his name is just J. You can clearly see that as J is getting his identity erased K is deleting his name one letter at a time, until he gets to the first one which is of course J. Also why whould he have the only name that was an actuall word, both K and L are single letters too, so don't question me.
As far as his name goes.... you have to be pretty blind to NOT notice (they even hold the camera on it for a few seconds) that after K erased "Darrel James Edwards", he leaves the "J", then smiles, then presses the Enter Key to which the computer comes back and shows us that it saved his new identity. While its saving the new identity, the screen clearly says (and when slipups.com starts showing images I will be able to prove this) "J". Also from any previous slipups, whenever they do the captions, sometimes they reword things for clarificaiton or maybe at the time they didn't know that the names were single letters. In the case of the MIB animated stuff, the guy doing the captions may not have even seen the movie and thought that the names were spelled "Jay" and "Kay".