When posting a game played on chess.com in a forum or blog post, is it considered good manners, bad manners, or neutral to leave the other player's name in?

Just don't do it. There are too many emotional chess players about that are easily offended. To avoid this, it's best to leave the opponent's name out.

I would leave N/A, or N.N for the opponents name.. but if you really want to, ask the other person first, because alot would get offended if they find out, unless of course, you lost or it was drawn.