What is the best way to get the child class name for use in a parent class
Looks fine to me; though somethings to think about. Do you need to run get_class? Or might it be better to have a model variable in the child class

class Blog extends Controller
{
    private $modelClass = 'Blog';
}


The overhead of get_class might be small, but probably more than a variable; but this way also give you the ability of being able to use the same model with multiple controllers if you need to. Granted you could just inherit with the models too, but that would mean 2 includes instead of one.

If you don't go that route, consider some validation, string tidying or consistency in your model/file names.

$path = 'models/' . $name . '_model.php';


will likely equal Blog_model.php but your class is Blog_Model see the mixing of cases; consider Blog_Model.php or doing a strtolower($name). This might seem minor, but different Operating Systems handle case differently and I have been bitten by this exact issue.

I noticed you are doing a require rather than a require_once which could lead you to have cannot re-declare class errors. if require_once isn't for you consider 

if(!class_exists($modelName))


This might seems abstract at the moment, but when I came to upgrade an admin system for a custom CMS I found it really handy for the admin Controllers to wrap the frontend wesbites controllers, and adding a little checking could greatly increase your flexibility further down the road.

If you haven't done already check out __autoload http://php.net/manual/en/language.oop5.autoload.php if might be more overhead, but it is just so handy I really miss it on legacy projects.