You're almost there, if you turned warnings on you would have seen that the interpreter thought you wanted to print to a filehandle. a tiny modification would've achieved what you're looking for, note the infix arrow operator in the print line..

use warnings
no strict 'refs';
my $sub = 'do_this';

print $sub->("Fred");


sub do_this {
   my $var = shift;
   return "My name is $var";
}

sub do_that {
   my $var = shift;
   return "My name is not $var";
}
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