Latest iOS 9 doesn't show WiFi symbol, even when connected to WiFi
It should show up so the fact that it doesn't indicates a problem. In the past, Apple has focused on reliability for newer models and then subsequently released a X.1 version with under-the-hood work done for older devices. So it wouldn't surprise me if it is a deeper problem. 

Two simple things to try right off would be a hard reboot of the device if you haven't already. You can do that by holding the home and power button down until you see the Apple logo. Also, make sure that you are on the latest version of iOS. iOS 9.0.2 is out now, so update and hopefully that will solve your issue.

If that doesn't work, you have to take it up a notch. You could try resetting all preferences to see if that solves the problem. Go to Settings - General - Reset - Erase all Settings to perform that function. If that doesn't work, the other main thing to try would be to restore the phone. Make sure you have a backup (I always like to have two), wipe the device, then restore.