UPDATE

But I don't know if this helps with exported vars, since IIRC "exporting" means copying a reference into the importing namespace. In other words: the current "fully qualified name" is from the importing namespace.

If you wanna find the original full qualified name you have to parse all loaded STASHes, till you find the reference. You can find the namespaces by inspecting %main::

print join "\n", grep {/^.*::$/} keys %main::

-->

Tie::
utf8::
TST::
re::
DynaLoader::
mro::
strict::
Regexp::
Term::
UNIVERSAL::
overload::
Data::
IO::
Exporter::
Internals::
warnings::
Config::
DB::
CORE::
attributes::
Scalar::
vars::
XSLoader::
B::
main::
Carp::
PerlIO::
O::
bytes::
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UPDATE

or by checking %INC