What's the noun for palindrome? Here's the word you're looking for.
palindrome
A word, phrase, number or any other sequence of units which has the property of reading the same forwards as it does backwards, character for character, sometimes disregarding punctuation, capitalization and diacritics.
(by extension) A poetic form in which the sequence of words reads the same in either direction.
“A palindromist in his own right, he had this to say about quality palindromes.”
“Laymen often assume that the palindromist chooses a topic and then suddenly an entire symmetrical phrase emerges from his subconscious, spontaneous and complete.”
“I also subscribed to journals such as Logophile, Verbatim, Maledicta, Cryptologia, Semagames, Wordsworth, and The Palindromist.”