Is it an external app you receive the intent from? You could use the getReferrer()
method of the activity class
A simple example: I opened google map app to share some location with my app by using the share option of google maps. Then my app opens and this method call in the Activity:
this.getReferrer().getHost()
will return:
com.google.android.apps.maps
see documentation here: https://developer.android.com/reference/android/app/Activity.html#getReferrer()
Note that this requires API 22. For older Android versions see answer from ajwillliams