Using the xml_split and xml_grep that come with XML::Twig, you can do this in one (long!) line:

xml_split -l 1 tsplit.xml \
&& perl -e'my @src= glob( "tsplit-*.xml"); \
          foreach my $target (`xml_grep -t name tsplit-*.xml`) \
            { chomp $target; \ 
              my $src= shift @src; \
              warn "rename $src, $target.xml\n"; \
              rename $src, "$target.xml";
            }'
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Replace tsplit.xml by your file name of course.