Certificates that identify the owner of the site are Extended Validation certificates. They require certificate authorities to check the owner identity, and are as such more expensive than certificates that don't.
A normal certificate only ensures that the website you are talking to is indeed the domain you tried to contact.
Confirms that the possessor of the certificate owns the domain that
is displaying it.
Serves as the public-private key combination for encrypting traffic.
Is issued by a Certificate Root Authority (CA) OR an entity that has
been granted subordinate status to a root CA.
Users can override protections: If you navigate to an HTTPS site and
your browser cannot verify the certificate (perhaps because it is a
self-signed certificate), you have the chance to continue and
instruct your browser to trust it anyway.
An Extended Validation (EV) certificate (when used with an EV aware client):
Subject to stricter verification requirements to prove the identity
of the holder and the holder's connection to the domain name. These
requirements are detailed in pubished guidelines, especially
Section 11, Verification Requirements.
Is embedded in the browser by the browser vendor.
Limited by how long they are valid. Maximum is two years. Holders
must go through verification process again after time limit.
No wildcards allowed.
The ordinary user cannot add these to the list of trusted
certificates in the browser (so, not possible to self-sign these).