Yes, as required by USCIS, Form N-400 applicants must write the names of all their children on the application form. USCIS also specifies that the applicant must indicate their children that are:
- Stepsons or stepdaughters;
- Adult or minor (under 18 years of age);
- Born outside marriage or a legitimate child;
- Living with you or separately;
- Born on the United States territory or outside the U.S.
You need to provide all the information about your children in the part 11 of your Form N-400 application.
Make sure that you also provide biographic data about your children, including their Alien Registration Number (if available), date of birth and country of birth, living address, and their legal names.
If the application form does not have enough space for you to mention all your children and their information, you still have to provide their data. You need to use a separate sheet of paper to provide all the data.
You should not conceal any data about your children that USCIS requires on the application form. Otherwise, your application for naturalization may be rejected. Besides, if you mention all the children and their data, it will be easier for your children to naturalize in the United States in the future.