Can a person be prosecuted if the arresting officer did not correctly identify the name of the store that the misdemeanor occurred? The charge is larceny for a 17 year old 1st time offender?

You probably mean will the judge dismiss because of a technicality ? I hope not, because the offence still occurred no matter where it was, and of course there would be have been store witnesses, so that would over rule the mistake by the officer.

Normally no, if there is evidence to the actual crime, having the name incorrect will not have any bearing, The officer can merely add a amendment to the police report showing the error.