You are quite correct in that I haven't addressed mnnb's primary request; however, I did state my intention: "This may not be exactly what you want but should provide some direction: ...".

There were so many issues with the posted code (e.g. "sub name_search(@_, $search_string) { ... }" and "$run_time = time() - our $start_run;") that I chose not to attempt to make this code (in its present form) faster as that didn't seem like a useful exercise.

Beyond that, I can only echo what ++AnomalousMonk wrote in the first response to your comment.