There’s no reason for palindrome to actually be palindromic, because it’s built from a Greek base (palindromos) meaning to run back – I mean, it’s not an invented word cleverly designed to be what it describes. For that sort of thing, we have to look to emordnilap.
Emordnilap is not a recognized word. But it has a cult following, and that’s what got “selfie” in the dictionary. Our language is a living one, with branches that grow, change, and die off year after year.
Emordnilap is palindrome in reverse (which, when you think about what palindrome means, is like holding a mirror up to a mirror), and describes when a word is a wholly separate word in reverse. Think pots and stop, rats and star, and so on. You can Google search for more.
While I am tickled at the idea of emordnilaps, what I think would be really interesting is the same thing across languages. A word forward in English is a Spanish word when reversed, for example. I have no idea if those words exist (and my utter lack of lingualism is a real barrier here) but I’d be thrilled to find out they do.