I'm sorry, but I can't imagine this happening. First, even the densest idiot realizes multiple people can have the same name. Unless you work for a literal retard, I don't think you'd have a problem.
And besides that, getting a DUI fucks up your life a lot more than getting your name posted to twitter. Little things like having your license revoked, getting thrown in jail, and spending a bunch of time in court. Again, unless you work for a retard, your driving into work should tip them off that it wasn't you.
Worst case scenario is your boss says "I see you got a DUI" (as if he's following that twitter account, lol), then you whip out your license and prove him wrong. Maybe a 30 second inconvenience.