Is it a crime to publicize someone's SSN with their name?

Your question is entirely not clear and can yield different answers with additional information. I you run out in the street in Brooklyn and publicize (yell out) someone's name and social security number, you will not be criminally charged because New York has no such crime of yelling names and social security numbers in a street. You may be charged with disorderly conduct and taken to a hospital for psychiatric observation and nothing else. If you are a personal banker at Chase and you hand out customer names and social security numbers to passers by, you will likely only be fired and banned from any further bank work. However, if you sell customer names and social security numbers for the purpose of identity fraud, you will trigger New York State and federal law that will lead to your prosecution. Perhaps if you describe a full and complete fact pattern, you will get a more precise answer - maybe with code sections - that will be more useful to you.