Your employment status will not affect your naturalization application and you may change jobs after filing your naturalization application and it is perfectly fine to do so. Nevertheless, all the other requirements remain the same and you need to prove that you meet those requirements. The adjudication of your naturalization application will depend on your moral character and on the other eligibility requirements and not on your job and your naturalization application will be approved, even if you do not have a job. If you change your job after filing Form N-400, Application for naturalization, you may just inform the USCIS officers during the naturalization interview, about your job change and provide information about your current employer. And there is no separate process to inform the USCIS officers about your job change after filing your US citizenship application.
The outcome of your naturalization interview may not depend on your employment status and it is perfectly ok to change jobs after filing Form N-400. You need to provide details about your employment in the 6th part of the naturalization application. You must provide details about all your previous employers and you must first enter the name of your current employer and then the names of the previous employers. If you need more space, you may use a separate sheet of paper and attach that to your naturalization application. You should write the names of your previous employers and the full address of those employers. Similarly, you will have to mention the dates and your profession.
During the naturalization interview, you may be asked few questions about your employment status, just to make sure that you were not fired for committing crimes. If you have valid reasons for job change and if you have not committed crimes, you may not be at risk and remember that people with criminal background will not be granted US citizenship and if the reason for job change is due to committing crimes, your naturalization application will be denied. However, see to that you complete your US citizenship application accurately and submit all the relevant supporting documents. If you have filed your taxes and if you have not involved in criminal activities, your naturalization application will not be affected by your employment status.