How do I put the My Company name on the navigation bar like this on my site:
This is a feature when your site uses an Extended Validation SSL (SSL) Certificate, which, in addition to displaying a green lock, also displays the company or organization name of the site in green.
EV (Extended Validation) advanced validation technology allows browsers from Internet Explorer 7, Firefox 3, Google Chrome, Opera, and KDE show the address bar in green with the name of your business, allowing users to identify your site as safe, authentic and not cloned. Font
To have the certificate on your site, you need to purchase it from a company that specializes in digital security and hosting services and install it on your hosting.
Just to name a few companies that provide the certificate:
As it appears in some popular and modern browsers: