Find the Instance Name , Port on which SQL Server is Listening

SQL Server is sometimes installed as named instances and sometimes will be made to sit on different ports.

The host name , Server name and the instance name can be identified by the SQL functions

SELECT SERVERPROPERTY('servername') ServerName
 ,SERVERPROPERTY('InstanceName') instancename
 ,SERVERPROPERTY('MachineName') AS HOSTNAME

For the Port number you can read it from the Registry or the ErrorLog

Registry:

SET NOCOUNT ON

DECLARE @key VARCHAR(1000)
 ,@PortNumber VARCHAR(20)

IF charindex('\', CONVERT(CHAR(40), SERVERPROPERTY('servername')), 0) <> 0
BEGIN
 SET @key = 'SOFTWARE\MICROSOFT\Microsoft SQL Server\' + @@servicename + '\MSSQLServer\Supersocketnetlib\TCP'
END
ELSE
BEGIN
 SET @key = 'SOFTWARE\MICROSOFT\MSSQLServer\MSSQLServer\Supersocketnetlib\TCP'
END

EXEC master..xp_regread @rootkey = 'HKEY_LOCAL_MACHINE'
 ,@key = @key
 ,@value_name = 'Tcpport'
 ,@value = @PortNumber OUTPUT

Error Log:

USE master
GO

xp_readerrorlog 0
 ,1
 ,N'Server is listening on'
GO