Lexical (my) variables are not stored in the symbol table. You could, however, make a hash of references to the variable names. Then, with some dereferencing,

my $test="my_variable_name"; #imagine this is a hash key
my $default_value="the value I set"; #while this is the hash value

my %hash = ($test => \$default_value);

print "the value of \$$test = ${$hash{$test}}\n";
${$hash{$test}} = "A new value";
print "the value of \$$test = ${$hash{$test}}\n";
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I'm not sure this demonstrates what you want to do, but hopefully it gives you an idea about how to approach it.