I _think_ that the commenter can use their Wordpress account as an OpenID to log into LJ (I know at one point I used my LJ as an OpenID to log into Dreamwidth & comment there on various accounts). From the account drop-down options here on LJ, it looks like you could use a Facebook, Twitter, or Google account to log in as well. It would at least avoid the "anonymous" option. If you can't change from the comment page, it may help to go to the main LJ page, and try logging in there.