The invitation to run, to play, is just blatantly obvious in her posture. Ammy may be pretty clearly a goddess right now, with the boost from all the love and praise from her world recently, but she's still a canine. What better way to make friends?

"I'm delighted to see another wolf arrive! I am Amaterasu, Guardian of Nippon." Proper introductions should be given regardless, especially right now when pretending to be mundane is particularly difficult.