A way to do it is with a predicate.

BEGIN {
    package Person;
    use Moose;
    use overload '""' => sub { +shift->show_person }, fallback => 1;

    has 'name' =>
        is  => 'ro',
        isa => 'Str',
        required => 1;

    has 'age' =>
        is  => 'ro',
        isa => 'Str',
        predicate => 'has_age';

    sub show_person {
        my $self = shift;
        join(", ",
             $self->name,
             $self->has_age ? $self->age : "age unknown");
    }
    __PACKAGE__->meta->make_immutable;
    no Moose;
    1;
}

my $person = Person->new({ name => "Bob" });
print $person->show_person, "\n";

print Person->new({ name => "Your Uncle",
                    age => 93 }), "\n";
[download]

More here: Moose::Manual::Attributes.

(Update: man! I waited for hours to see if anyone would bite on this and when I finally go to post, FalseVinylShrub hit create while I was typing.)