Ruby, I don't really understand what your question is - Google is a search engine which indexes online information which is publicly available, which would include criminal convictions if they been reported in a local paper, for example.

This information is not private - convicted offenders can and often are named in public depending on the circumstances - somebody getting a speeding ticket is unlikely to be, but that's because the information isn't likely to be published anywhere as it isn't very interesting, not because the press are precluded from doing so. Google can only search for and find what's there, whether it's a conviction or a birthday announcement in the local rag.

The way to do this is to type in the name and press Search, and if there is anythere there for it to index it'll probably come up somewhere. There are far better hobbies, honest.