Why do some websites show the company name next to the URL?

This is only for websites that use Extended Validation SSL encryption. The name is the name the certificate is issued to. It is a security feature put in place to verify that the website is actually served by the company it claims to be from. Simply put, it works like this:

• Company X decides it wants to secure (e.g. by encryption) communications with the website and the one who requests it.
• Company X asks a trusted third party to verify the owner and to issue a digital certificate.
• The third party checks the applicant and then issues a certificate, vouching for the identity of the website. So you know Github is actually Github, and not some malicious website.
• Your browser sees that Company X uses EV SSL-encryption and queries the certificate. This shows to be issued by a trusted third party to Company X. Your browser then displays the name of the company the certificate was issued to. If it is the same, it will turn green (like in your screen shot) if it does not, the browser will warn you that the website might not be the website it says to be and turn red.

You need a couple of things to set this up, most notably:

• An EV SSL certificate (Like from Godaddy, but there are many more issuers out there. Google this for yourself.)
• A host that supports the use of SSL (inquire with your host on how to set this up for your domain)

Certificates generally don't come cheap, and it is really a matter of whether you really need it. Admittedly, it looks cool, but it might be unnecessary for you.

You can find more detailed information about this from other sources, like its Wikipedia page.

That's a result of using an Extended Validation certificate - extended validation, or EV certificates require additional validation before the certificate is issued. The idea is that there is better proof that the company really is applying for the certificate, so you should be able to have some more confidence that you really are talking to who you think you are.