I want to thank Alex Diaz for coming up with the solution. Here are the steps I took to resolve the problem.
1. Configure a client alias via Configuration Manager. This requires the listener port, which takes care of the issue with Named Pipe connection resolution.
2. EXEC sp_addlinkedserver '<Server Name>', N'SQL Server'
GO
3. exec sp_addlinkedsrvlogin @rmtsrvname = '<Server Name>',@useself = 'false',
@rmtuser = '<User Name>', @rmtpassword = '<User Password>'
GO
Hope this helps anyone else that may be fighting this battle.