I am going to change my checking account because I expect a writ of garnishment to occur soon because I did not pay a judgement against me.How can the lawyer legally get the information my new checking account for now and every time I change my bank account? Can he just keep serving me post judgement requests to disclose all bank information?

When you open the new bank account they run a "check" on you for bad checks and other problems. This shows up, so they can see everywhere you apply for a new checking account within minutes of you doing it, if they check

The bank will notify the government of your new account. You can thank the Patriot Act. Unless you somehow provide fraudulent information, you can expect that they will find your checking account.

Probably a good time to set up a realistic payment schedule...