$name = "(\.dll|\.exe)\$";
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As a minor point, I wouldn't use capturing parens where not needed, I'd write

my $name = qr/\.(?:dll|exe)$/;
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instead. And as you can see from this line itself, I wouldn't put into a string to interpolate it later, but I would create Regex object, especially since it isn't supposed to change. But then I wouldn't probably create any intermediate variable, in this case, that is:

find sub { push @files, $_ if /\.(?:dll|exe)$/ }, @dirs;
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