On the subject of Xiao Xingchen not quite understanding how off-mountain life works (as @orodrethsgeek put it, he “is just slightly out of sync with the rhythms of the world,” (see also: giving all your money to beggar girl)), my favorite current example may be how he introduces himself to the gang at the Chang manor:
Not, “I’m Xiao Xingchen, student of famed immortal Baoshan Sanren and this is Song Lan of Baixue Temple” or even, “I’m Xiao Xingchen, the bright moon and the gentle breeze and this is Song Lan, the distant snow and cold frost.”
Just, “hey everyone, I’m me, that’s my friend him!”
The only thing about them that matters is how they’ve just acted, with the small allowance that Xiao Xingchen would also like to note that Song Lan is his friend. (cute.)
This is not how cultivators introduce themselves. Cultivators introduce themselves with their sect affiliation or other identifying information. They bow, usually with their swords in hand. Xiao Xingchen and Song Lan don’t bow until Lan Wangji initiates one in a moment, which he does, because, in spite of Xiao Xingchen’s thoroughly unhelpful introduction, he recognizes them.
But that’s not what’s important to Xiao Xingchen and Song Lan (and Song Lan has no excuse, unlike Xiao Xingchen, he must know social conventions are being broken and is happy to let Xiao Xingchen do the speaking anyway).
Here is what is important to Xiao Xingchen and Song Lan:
a) they have apprehended a violent criminal
b) these friendly young cultivators have helped them do so
a means they are good people and they trust Lan Wangji, Wei Wuxian, and Jiang Cheng to see that. b means that Lan Wangji, Wei Wuxian, and are good people they can trust as well. (And that’s fortunate because here’s what Xiao Xingchen and Song Lan are not interested in: actually delivering said violent criminal to politically expedient justice.)
It’s really a lovely illustration of just why they want to start their own sect. One free of political ties and bloodlines where the only thing matters is how they help people. Xiao Xingchen is always eminently gracious but he lacks social graces.
But honestly, it’s a good thing he and Song Lan are famous enough, because otherwise there as no guarantee they’d get away with the whole, “hello, nice to meet you, doesn’t matter who we are but please take this violent criminal off our hands so we can go back to wandering the world and saving people” schtick.