Use the translate operator (see tr/SEARCHLIST/REPLACEMENTLIST/cds) to delete the spaces, then use a case insensitive match. The code below captures the matched string to retain the original case, but doesn't attempt to figure out the "spacey" version of the match:

use strict;
use warnings;

my $x="My name is VC";
my $y="myname";

$x =~ tr/ //d;
print "Matched: >$1<\n" if $x =~ /(\Q$y\E)/i;
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Prints:

Matched: >Myname<
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