Though it sounds a little dangerous to be reading variable names in from a file, if I had to do it I would probably just push one more layer of abstraction into the datastructure. That is... something like this:

my %name = ( this => 1, that =>2 );
my $storethis = { 'name' => \%name };
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...and then store that structure.... its name is the name of the only hash key in the top level.