Following on from the question about Jon’s name – would it not have been dishonourable to name a bastard named after you? Do we see it elsewhere in the series outside of the Freys?
Also, is there any chance Jon knew the truth of Jon Snows true parentage?
Not really. It’s not like Jon’s at court or Ned is asking Jon to be his godfather or something, so the issue of honor (I’d go more with insulting/not insulting) doesn’t really arise.
And there is zero chance that Jon Arryn knew the truth. The only person other than Ned who knew the truth was Howland Reed and maybe the Daynes; Benjen might have guessed the truth, but I don’t think Ned ever confirmed it to him.