Her name never appeared, not in the original, only the monster in the tree was written in the TV cast.
Regarding the following questions, I can only say that she should live in that tree, so she should still be there, otherwise she could have followed Natsume that year ... I don't know if I have seen her since. After all, the original and TV only appeared once. After all, she is not in the town where Natsume lives now.
This is the fourth episode of the third season of Natsume. After watching that episode, you should know that she was deeply impressed by Natsume. After all, few people can see her, so she actually cherishes the time with Natsume, so she always remembers Natsume. She just likes to miss her and has nothing to do with romance.
PS: It's purely personal. Just have a look.