My middle name is Ann. I want my checks to say P.A.Myers The bank says they should say “Patricia Piper Myers”. Piper is my maiden name.
The recipients of your checks typically have no idea what your ID says nor should they care what you call yourself. I have checks that just have my last name with no address and that has never caused an issue. If you are paying by check in person the recipient could ask for ID and may hassle you about the mis-match, but I'm skeptical that would be much of an issue these days, I've not been asked for ID when paying by check in years.
When you are the recipient of a check, it's best if the check is made out to your name as it appears on a form of ID, since confirming the check is intended for you is part of the check cashing/deposit process.