Update 22 Dec 2013: This feature does not seem to be working in Sense 5 after I updated my HTC One X to Android 4.2.2.
While putting in contacts in my phone I generally put the Company name also. But to search by Company name you need to enable a setting which is not enabled by default in your People app of HTC One X.
Go to your People app and open the menu. Tap on "Settings".
