Using what you said as a template, I've come up with this so far:

 #!/usr/local/bin/perl
 open (MYFILE, 'shoplist.csv');
while (<MYFILE>) {
     chomp;
     if (/\"(.*)\"/) {
         my ($first,$last) = split('\s', $_);                         
+             
         print "$last $first\n";
     }
 }
 close (MYFILE);
[download]

It's working decently, how do you get rid of commas and a double quote in a line? For example, the names are coming out like:

Last, "First

I'd like to remove the comma and the double quote so I can just have the last and first name. I'm getting pretty close, all that's left is to figure out how to save the middle initial!