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.
from The Century Dictionary and Cyclopedia. To designate by a mistaken or unsuitable name; misname. n. A misnaming; the act of applying a wrong name or designation. n. In law, an error in name; misstatement in a document of the name of a person. n. Hence A mistaken name or designation; a misapplied term.