USCIS will send you notifications regarding the processing of your case upon completion of each stage. However, if you do not want to wait, you can check status of your Form N-565 yourself using special online service.
When you submit paper version of Form N-565, you receive a mail from USCIS containing acceptance notice with Application Receipt Number and instructions on how to create and use a USCIS online account. When you decide to file Form N-565 online, first you have to create your USCIS account, and then upon submission of the Form, such acceptance notice will be posted to your account.
USCIS assigns a unique 13-character Application Receipt Number to each Form N-565 they receive. And this number will help you to check the status of your case online on the official USCIS website (egov.uscis.gov/casestatus/landing.do). You will have to simply enter your Receipt Number into the field and click button “check status”. Note that you should not include dashes when entering the Receipt Number.