use strict;
use warnings;

my $Name = '[A';
my $SearchInHere = "FredJimBert[A";

print "Matched quoted\n" if $SearchInHere =~/\Q$Name\E/;
print "Matched raw\n" if $SearchInHere =~/$Name/;

##</code><code>##

Unmatched [ in regex; marked by <-- HERE in m/[ <-- HERE A/ at noname.pl line 8.
Matched quoted