When we take a report, we don't always require positive ID. Of course, that depends on the nature of the report. When I arrest someone and they have no ID, I have to use the name that they give me. Then, once they're fingerprinted and we get their true identity, the name they gave becomes a part of their criminal record.
Depending on the nature of the report it might be fairly simple. However it is illegal. In most states it's a misdemeanor. In some cases it could be moved up to a felony if in conjunction with a criminal offense.