I think Gwen assumed that it was just a name being used twice - King Olaf's daughter and Morgana's mom are both named Vivian, after all. And, Gwen was basically already leaving when Morgana gave her the neckerchief thing, so I think that at this point, it's at least partially Morgana trying to salvage an old friendship - the only one which doesn't have any weird mind games involved, only some copious amount of lying.