It is the fear of long words. Also spelled sesquipedalophobia. It is recognized in formal writings.
It come from the word sesquipedalian which is a long word or a person who uses long words.
A synonym is hippopotomonstrosesquipedaliophobia which is controversial and itself derived from sesquipedaliophobia. It takes the Greek-derived word hippopotamus (hippo-"horse" compounded with potam-os "river", originally meaning "river horse") and combines it with monstr from Latin monstrum (monster), the Latin sesquipedali, and the Greek phobia (fear). It is intended to exaggerate the length of the word itself and the idea of the size of the words being feared.