pseudonym: is a fictitious name assumed, esp. by a writer, as for anonymity, for effect, etc. (Webster's New World)
Of course there are degrees to the degree of anonymity anyone might want or care about. I guess Rice doesn't care, or she doesn't care now, anyway. Some people have wanted various degrees of anonymity for various reasons. For Pessoa, it was a different situation entirely, he was already obscure, he didn't need anonymity. He thought these "heteronyms" were other people with separate lives. They were sort of his imaginary literary friends (although they tended to dislike each other, and give negative reviews of each other's works). And they write very different poetry. He also wrote poetry in his own voice as well. It's as if he's the Portuguese T.S. Eliot, Ezra Pound, William Carlos Williams and Wallace Stevens (and more) all wrapped into one person. He's really become the most important figure in Portuguese literature (Camoes, please forgive me!).
And yes, you got it about the premise of the novel, Reis is a separate human being who lives on. Of course he is grief stricken, he has lost his dear friend and correspondent. It's really sad.
Pessoa being queer and all, I sort of get the feeling that he was sort of inventing imaginary boyfriends for himself, or at least inventing his own little gay literary community. I don't know if anyone has analyzed the relationship between the heteronyms from this point of view.