The search feature is not very good. Best to browse through names listed for each year indexed. Is possible that surname might have alternate spelling.
They do have some naturalizations indexed up to 1923. If your ancestor might have migrated for example 1900....earliest date to look for naturalization would probobly be 1905 - up... I think the later migrations had 7 year wait...but don't quote me on that...
Make sure you check index's for all court records listed.
Illinois also has some naturalizations indexed for East St. Louis Court 1874-1906
Also some marriage and death records indexed at ^.