An awk way:
$ awk 'NR==FNR{a[$1]=$2;next} {print $2,a[$3"."]}' managers employees
Fred
Billy Fred
Sally Fred
Jim Bill
Jane Bill
Sue Sally
Meg Sally
An awk way:
$ awk 'NR==FNR{a[$1]=$2;next} {print $2,a[$3"."]}' managers employees
Fred
Billy Fred
Sally Fred
Jim Bill
Jane Bill
Sue Sally
Meg Sally