I wouldn't worry too much about it. I've stopped several people with the same names and ages of people with warrants, suspended licenses, etc. They very rarely have the same date of birth, and you have to match the social security numbers as well. I know there's someone else in my state with my same name, and it's a pretty rare name.
I doubt this person knows or would think to look to see if you existed. Usually the identity thefts come from stolen social security numbers, financial cards, or confidential applications, etc.
I would just keep an eye on my credit, bank statements, and such to make sure everything is ok. Everyone should do that anyway regardless. Usually people with your problem do tell me about it when I stop them and are pretty worried as well. Make sure you carry your ID with you just in case, but it's probably nothing to stress over.
"The inherent vice of capitalism is the uneven division of blessings, while the inherent virtue of socialism is the equal division of misery." - Sir Winston Churchill