I've written on this subject in the past:
<a href="http://www.chetson.com">Raleigh criminal lawyer</a> Damon Chetson represents people in Raleigh, Cary, Apex, and the rest of Wake County, North Carolina. The information provided here is for educational purposes only and should not be relied upon as the specific facts may change the potential advice. Consult with a licensed <a href="http://www.chetson.net">Raleigh criminal lawyer</a> or <a href="http://www.chetson.com">Raleigh DWI attorney</a> in your jurisdiction about your legal question or problem. For a free consultation about a North Carolina case, call (919) 352-9411 day or night, any day of the week.
There are a few potential options:
1) Ascertain whether or not the case could be expunged from your record. The idea behind an expungment is that there is no longer public documentation of the arrest and or conviction. Most of the expungement rules are governed by statute.
2) Find out from which website the google search is detecting the publication of your conviction. Google just searches websites that already have information. If your name was published in the regular course of a state case search website, then you may not be able to have that removed. (unless you are able to get the case expunged from your record as stated in option #1)
3) If neither option 1 or 2 is feasible in your particular situation, you may want to approach specialized website programs that focus on improving ones online reputation. There are many: www.reputation.com, etc.
4) If none of these work, then a) play ignorant and act like somebody may have used your name if confronted with the situation and b) if that does not work, just make up a fantastic story about you having to save the world or a family from a burning building and you had no choice but to drive after consuming a few drinks.