You can configure your application to automatically record all incoming streams. You will need to edit your application's Application.xml file and use the following STreamType in the /Root/Application/Streams/ block.
There is not a configurable way to change naming conventions of recordings using StreamType live-record, but you can alter the file name of the recording programmatically when it is done recording using IMediaWriterActionNotify
You may want to look into using the HTTP Live stream record feature. This has more recording and file naming options.