my $method = $$rs{row}{field_name};
my $rv = $object->$method();
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or

my ($rv) = map { $object->$_() } $$rs{row}{field_name};

or

use List::Util qw( first ); # core since Perl 5.7.3
my $rv = first { $object->$_() } $$rs{row}{field_name};
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or

$object->$_() for $$rs{row}{field_name};, if you don't need to save its return value.