There's no 'of course' about it....neither Pugs1957 nor any of us here can possibly know whether you are the legitimate owner. The problem you are encountering normally only occurs when, for one reason or another, an account has not been removed from a device by that account holder. Did you buy new?
Did you first put your Google account details on the phone, and then Factory Reset?
Or did you first Factory Reset, then try to add your Google account?
Also, did you buy online, or from a store? If the former, was it a private seller, or a retailer?