What Host Name is my application connecting to SQL Server on
Assuming you can install the app on a Windows 7 (or higher) workstation you can perform the following steps to determine exactly what server and IP address the app is using:


Start a cmd.exe prompt "As Administrator"
Run "ipconfig /flushdns"
Run the app, and ensure it connects to the server
From the cmd.exe prompt, run "ipconfig /displaydns" 


The output from step 4 will show all host names, along with the IP address(es) for those hosts that have been resolved in step 3.  Try to ensure nothing else is running between step 2 and step 4 to narrow down the results displayed in step 4.