If your running an HTTPOrigin application, then yes, httpRandomizeMediaName is set to "true" by default.
Here is a bit more detail about this property, and how to edit it:
Set this property to true to help to ensure that the chunks in live streams are unique if the encoder is restarted.
Wowza Streaming Engine Manager configuration
In Wowza Streaming Engine Manager, click the Applications tab, and then click the name of your HTTP origin application in the contents panel.
On the HTTP origin application page Properties tab, click Custom in the Quick Links bar.
Note: Access to the Properties tab is limited to administrators with advanced permissions. For more information, see Manage credentials.
In the Custom area, click Edit.
Click Add Custom Property, specify the following settings in the Add Custom Property dialog box, and then click Add:
Path - Select /Root/Application/LiveStreamPacketizer.
Name - Enter httpRandomizeMediaName.
Type - Select Boolean.
Value - Enter true.
Click Save, and then restart the application to apply the changes.
Use a text editor to open the [install-dir]/conf/[application]/Application.xml file for your HTTP origin application and add the following property to the <LiveStreamPacketizer>/<Properties> container. Be sure to add the property to the correct <Properties> container in Application.xml as there are several such containers in the file.
Restart the Wowza media server software to apply the changes.
]Note: If you want to use Wowza nDVR as an HTTP caching origin, you must also add this property to the Root/Application/DVR path (<DVR>/Properties container) to your live application that has Wowza nDVR enabled.