Can there be two people with the same name, social security number and birthdate?

I just found out that there is someone else with my name who uses my social security number and has my birthdate, several states away from me. It seems to me that it is identity fraud, but my credit report checks out fine from all three credit reporting agencies. Is it possible that there could be a double, legitimately? Through some weird mistake? Or has my identity been stolen and I caught it before they could do damage? What should I do?

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