There are legitimate questions with her citizenship, anyway, IMO, regardless of false name, which would just add the the CF.
This is the, info AFAIK:
Father came to US in 1995. Would mean Father can become citizen in 2000 and all minor children can derive US citizenship when father gets citizenship. Minor children would be under 18 at time father was issued citizenship.
Omar's birthday on original MN state legislature page was 1981. It was changed to 1982 after reports surfaced about citizenship issues.
1981 birthday would mean she was too old to derive citizenship from father and would have to go through naturalization procedure and there should be records of her doing that.
That's info as I know it. There may be loopholes/exceptions, etc. that I overlooked or don't understand well enough.