If you get your application in before Jan 20th, they aren't going to care about previous names. They need to know them and have them on file, I guess, but only your current legal name will appear on the passport.
But, if you lie on the application (even by omission) and say you have no previous names to report, they will care a lot. Maybe they never find out, but if they do, your passport will likely be cancelled. It's not worth it.
Just swallow the dysphoria and complete the form truthfully.