Name should not play a role IMO.... I mean by barton's logic he ought to be a fan of Stefan-os Tsitsipas too, lol...
Name should not matter.
Even Damon respected Elena's choice, thats why he gave her back her necklace so that he wanted his relationship with her to be organic and not forced like it was with Caroline. By the way, Caroline herself had a thing for being slightly slutty in S1 and that Vickie, she was a complete slu-t. Damon treated these women badly, yes but they were not that classy to begin with and they were looking for trouble by hanging out with the wrong crowd. He always treated Elena well, so he did respect her choices most of the times, at times he did not and that was for her own good. Stefan saved Matt and let Elena become a Vampire, how great was that ?
Lets not pretend Stefan was that great, yes he was a gentleman and good in S1, we get it but he too did questionable things.