It can also be translated as "this is a hat" since there's no subject in the sentence. Either way, pretty amusing text to have on something you wear.
Y-yeah... thanks.Could you...tell me your name?I...I'm...I've already known.I'm a hat.Mokou.Fujiwara...Mokou.I didn't ask before because we had our hands full, but...That's a marvelous name...