Why didn't Taki write his name on Mitsuha's hand? When Taki meets Mitsuha by the shrine, just before the meteor strikes the town, Taki tells Mitsuha that they should write each other's names on their hands.

Instead of writing his name, Taki instead writes "I love you" on her hand, leaving Mitsuha with no way to remember his name.

Why didn't Taki write his name on Mitsuha's hand?
I think it was a sweet gesture that showed a little insight into Taki's character. It shows that he is young, in love, and struggling to find a way to share his feelings with Mitsuha.

At that moment when an opportunity presented itself for him to confess without having to say it out loud (the horror! :D), he foolishly thought it was more important to tell her how he feels than what his name was.

Very frustrating, probably done on purpose by the writer but not completely baseless.