I suspect that this question will really only be answered by force of necessity. Pluto was considered a planet until a number of other similar objects were discovered that reclassified it as a new kind of object.
Similarly with moonlets; they will be followed and named as moons until it is clear that there is a separate class with a clear cut distinction. So far, nature seems to have solved this for us, since we have found no tiny natural objects orbiting Earth, Mars, Jupiter, or Saturn even though the environments of all these planets have been extensively explored by spacecraft. Likely, non-gravitational forces from sunlight and solar wind keep pushing them in the same direction until they eventually get into an unstable orbit or crash into their primaries.
Until a clear reason for a class separation is found, I see no reason to look for one. If people take the trouble to work out the orbit, then objects of any size can be counted as moons. Currently, 22,000 pieces of space junk are being tracked in orbit around the Earth, and the computers are certainly up to the task of keeping track of them and, presumably, giving all of them names or numbers. In this case, we know they are all artificial, but we could name and track them just the same if they were all natural.
Of course, there's a valid economic reason to track all the space junk in orbit around the Earth, so to predict and possibly prevent collisions. Around a planet such as Saturn, there would be less reason to track thousands of pieces of debris even if they were ever found. So the ultimate answer to your question is that they're moons unless and until there are too many to make it worthwhile to track them. Then they're just rubble or rocks or debris. Moonlets would be too fancy a word for such objects.