Daphne Bridgerton & Xie Yun
Depending on where a person was from then, yes, it could be construed as rude to be doing something else while someone was addressing the other person. That does not, however, stop him from giving her a bright smile.
"I'm Xie Yun." She deserved a proper introduction after all. Especially if they were going to be sitting down and talking for five minutes. "I've been doing rather well this evening. I can't complain, at the very least."
"I'm happy that you had something to preoccupy your time until I showed."