SharePoint 2010: Change the Public URL of a Web Application

First, go to central admin on SharePoint and click to "Configure Alternate Access Mapping". Change the URL that you want to a name that the company wants to have.

Then go to IIS on the Application Server, where the SharePoint 2010 is installed. At the left side, choose your site, and click then on "BINDINGS"

Add a new one and fill in the information...

Then go to the DNS server ( actually Domain controller ) and add a NEW A or AAAA

As last, give the host the same properties as on IIS.

Perform an IIS restart and re-browse..

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official KB: blogs.msdn.com/.../how-to-properly-change-the-host-header-url-of-a-web-application-in-sharepoint-2010.aspx 
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