Generally, the word acronym is used to describe words/initialisms which use only the initial letter(s)/syllables of the original phrase:
An acronym is a word or name formed as an abbreviation from the initial components in a phrase or a word, usually individual letters (as in NATO or laser) and sometimes syllables (as in Benelux).
So, hypothetical 'Brex' would be uncontroversially an acronym, but 'Brexit' would only fall under this if you classify an entire word as an initial part of itself.
There is (minimal) precedent for including the end portions of words* in what is commonly called an acronym, take amphetamine for example: alpha-methylphenethylamine.
So, using this interpretation of 'acronym', one could call 'Brexit' one. But it's much more common to label such words portmanteaux or blends.
* or the entirety of the final word, depending on how far you want to split methylphenethylamine