If they do a fingerprint check it will show up. If they do a check by name and date of birth it is so close that it will likely show up.
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At the time of your arrest, or at least before arraignment, you were fingerprinted. Your rap sheet contains information other than the name you were prosecuted under. It has your address, your date of birth, and your social security information. I believe that any decent researcher seeking your criminal history will find it. Let's hope that they do not further ostracize you because of your use of another name.