When you give a filename in the output-path string, Blender will append .nnnn to it.
The filename string can also appear in the “stamp.” This name is, effectively, “the name of the strip,” and the mere fact that it consists of hundreds of individual files is just happenstance.
I always direct the different outputs to different subdirectories, in addition to assigning each one of them a filename prefix as above. If I need to completely throw-away all or part of a shot, I want to be able to select a particular directory and either throw the whole thing away, or select file(s) within only it and throw them away.
Also by convention, each of the source blend-files is in a particular directory, and within that there is a subdirectory which contains all previous versions of that blend. I basically don’t throw anything at all away, except blender-outputs other than “finals.”