User 'Domain-name\User-name' does not have required permissions. Verify that sufficient permissions have been granted and Windows User Account Control (UAC) restrictions have been addressed.

Error while trying to access Reporting Services Manager for a new installation of Reporting Services.

 As documented by TechNet, primary cause is that, on a new installation, only local administrators have access to a report server. To grant access to other users, a local administrator can use Report Manager to create new role assignments.

This fix worked for me:
Start IE browser by right-clicking and selecting Run as administrator. Then enter your Report Manager url, e.g. http://Server01/Reports_SQLEXPRESS2008. This should now get you to the Home folder in SQL Server Reporting Services. 

Once there, click on Folder Settings, to bring up the Security window, and then on the right hand side of the Security tab in the Group or User pane, there should already be a built-in user called BUILTIN\Administrators.

Click on New Role Assignment to add (in the format Domain\Username) any new user that needs access to Reporting Services Manager. Then select from one of the following predefined roles for the new user:

Browser:  May view folders, reports and subscribe to reports.
Content Manager: May manage content in the Report Server.  This includes folders, reports and resources.
My Reports: May publish reports and linked reports; manage folders, reports and resources in a users My Reports folder.
Publisher: May publish reports and linked reports to the Report Server.
Report Builder: May view report definitions.
 
In addition make sure intranet settings are enabled in IE. Even when typing your password in the authentication popup it may not work without intranet settings enabled.  See how to enable intranet settings here >>

Technet MS SQL Server Documentation >>

Very useful blog entry at The Code Attic >>

Cannot connect to [database name]. A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Named Pipes Provider, error: 40 - Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 53)

Server Name: Make sure you are typing server name (i.e. host name or computer name) correctly along with the proper instance name of an installed instance of SQL Server.

As, even using '(local)' or '(localhost)' can also cause this error:

Correct format is: Server-name\db-instance-name. e.g. Server01\SQLExpress2008

Also (if using Windows Authentication mode) make sure the format of the username is as follows: Server-name\User-name. e.g. Server01\Administrator