In test2::new, you say:

 my $lib = test1->new();
 ($self->{lib}) = ($lib->print_name());
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That doesn't cause any error, but it doesn't do what you want it to do. It leaves $self->{lib} == 1, which is what print returns at the end of test1::print_name.

Later, in test2::get_name, you try to use $self->{lib} as an object instance, but it's still just the number 1.

I'd fix this by changing the code in test2::new to:

 my $lib = test1->new();
 $self->{lib} = $lib;
 $lib->print_name();
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You could also eliminate a variable this way:

 $self->{lib} = test1->new();
 $self->{lib}->print_name();
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You could also "fix" this by having test1::print_name return $self instead of the value of print

sub print_name {
    my $self = shift;
    print "I forgot what went here";
    return $self;
}
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I don't like that solution personally since the return value isn't really related to the method, but having methods return $self whenever possible is common enough.