use warnings;
use strict;

my $customTextinPrePostScript = q(MyName='Custom');
while (my $line = <DATA>) {
    if ($line =~ /$customTextinPrePostScript/i) {
        print $line;
    }
}

__DATA__
hello MyName='Custom' foo
nothing
[download]

G'day JLowstetter,

Welcome to the monastery.

I'd use qr for that. See perlop: Regexp Quote-Like Operators for details.

#!/usr/bin/env perl

use strict;
use warnings;

my @lines = ("MyName='Custom'\n", "MyName!='Custom'\n");

my $re = qr{MyName='Custom'};

for my $line (@lines) {
    if ($line =~ $re) {
        print "MATCH: $line";
    }
    else {
        print "NO MATCH: $line";
    }
}
[download]

Output:

MATCH: MyName='Custom'
NO MATCH: MyName!='Custom'
[download]