Crossword puzzles flex one very specific piece of cognition--the ability to find words, which is also known as fluency. Fluency is a type of process based in the speech and language centers of the brain. So doing crosswords might help you get better at word finding, but that's the sum total of their positive benefits to your brain.
misnomer. n. 1. an incorrect or unsuitable name or term for a person or thing. 2. the act of referring to a person by the wrong name.
transitive verb. 1 : to blunder in the choice of mistook her way in the dark. 2a : to misunderstand the meaning or intention of : misinterpret don't mistake me, I mean exactly what I saidb : to make a wrong judgment of the character or ability of The army's leaders mistook the strength of the enemy.