The arrest may be under your name and date of birth in the criminal arena and thus employer may find out. Honesty is best policy.
The answer above is only based upon the limited information provided. The answer is limited and my review is likewise limited, and thus the response is not intended to be acted upon as legal advice. Although licensed in numerous states, I am currently only licensed to practice law in the state of Nevada. No attorney-client relationship is formed until you sign an attorney-client agreement with my office. Any information provided is for discussion purposes only and there is no attorney-client relationship formed. Only general legal information is provided. Each case is unique and accurate legal advise would require review of all details and documents for each specific case. It is possible that the comments here, while meant to be helpful, may in some cases not be complete or accurate.
Was the DUI in Nevada? If so, it is likely accessed when a check is run under your social security number. In this dayand age, we need to assume that a background check will turn it up. Disclose the conviction ahead of time. It will save you both ebarrassment and the possiblity of being fired if they find out you didn't disclose it.