The answer is no, as far as I know, there is no such word. The nearest is the palindrome, being a word, phrase or sentence that reads the same left to right and right to left:"able was I ere I saw Elba."; or "Madam, I'm Adam." These are the best known of these. They are only interesting enough to acquire a special word as a mild curiosity, difficult to make up but of no literary interest.
Come to think of it, "Madam" is not only a palindrome but one of your a ... what shall we call it?
schizonyms might do; schizo (σχίζω) is the Greek word meaning ‘I split’ as in schism. I cannot imagine a schizonymic poem being written. Perhaps it could be done. Would a reader understand it? Now there is a thought. It might be used for some sort of schizonymic code, to be decoded by picking out the schizonyms and fitting them together.