Hi Joe,
I’m confused about what you’re trying to do, so perhaps you could be a little more specific. If you are rendering a single image C4D will give it whatever name you list in the “File” window of the render settings. But if you are rendering an image sequence each successive render must be given a different file number in order to avoid overwriting previous renders. If you are expecting all the files of an image sequence to have the same name, but without different file numbers to distinguish them, you may be confused about the process. For more info on automating the naming and saving of files see the Help content under “Edit Render Settings: Save.”
For example:

If that doesn’t help, please clarify what you are trying to do and how you would like to name your renders and distinguish between them.