There are many ways to search a genealogical database. Have you ever searched a database without filling in the name fields, just other fields?
First of all, many names in records have been poorly transcribed. Sometimes only if you search for the individual by other identifying information, like age and location, will you find them with a search. For census records, you can use no name but perhaps the location, age range, birthplace, a parent’s birthplace and/or a parent’s name. Or maybe not the full name, just the given names or just the surname. Try different combinations. (And don’t forget the old standby of reading a whole county page by page. Sometimes this is what it will take.)
Consider that early birth records may have no given name, or a given name field with “Baby” or a variant.
Another situation to search without a name is to search for records using only a birth year range and parents’ names to reveal information about siblings, particularly daughters who married and took their husband’s surnames.
Be creative with your searches. Consider when you might try searching without a name, or with only a partial name.
Best of luck in your research.