i'll throw this in the 'alternative' pile, since i'm not sure it qualifies as 'easier'.

#!/usr/bin/perl -w
{
    local $/ = undef; # slurp.
    $_ = <>;
}

$nb = qr/[^\}]*/; # non-close-bracket
$nq = qr/[^\"]*/; # non-quote

while(  m/^Tag+ \s+ \{
            $nb
            \n\s+ Name \s+ \" ($nq \s $nq) \"
            $nb
          \}
        /msx ) {
    substr( $_, $-[1], $+[1]-$-[1] ) =~ s/ /_/g;
}

print;
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i hadn't heard of the substr() lval return trick until this thread; it's pretty useful. also hadn't heard of @- or @+ till digging around. felt i'd share.

re: earlier comment -- the $N vars are immutable, so you can't s/// them, sadly.