WP calls it Domain Mapping, but it’s actually redirect.
From my experience outside of WP, if I want my blog name.wordpress.com look like mydomain.com I would do Domain Mapping. My experience at WP was exactly opposite. When I sent the browser to mydomain.com, I ended up at name.wordpress.com. Usually it is called redirect.
Is it possible to hide name.wordpress.com and to see only mydomain.com?