After looking at you code for a while I trimmed it down to the following code. I suggest you use it as a starting point for rephrasing your question.

#!/usr/bin/perl
use strict;
use warnings;
use CGI ':standard';

print "Size of party? ";
chomp (my $size = <DATA> );

print "Party name? ";
chomp (my $name = <DATA> );

my @arrayPartyNames;

my @tableSize = (
    "tableSize2One", "tableSize2Two", "tableSize2Three", "tableSize2Fo
+ur",
    "tableSize2Five", "tableSize2Six", "tableSize2Seven", "tableSize2E
+ight"
    );

exit if $size > 8 || $size < 1;
my $randomInt = int(rand 11);
my $time1 = 30 + $randomInt;

unshift(@arrayPartyNames, $name);

foreach my $table (@tableSize) {
    next if -z $table;
    
    open FILE, '>', $table;
    print FILE "$arrayPartyNames[0]";
    close(FILE);
    print "\nYou have $table reserved.\n";
    last;
}

__DATA__
2
Joe
[download]

Prints:

Size of party? Party name? 
You have tableSize2One reserved.
[download]