so your solution is that they should mess up their kids names instead what kind of purpose is that? a better solution is to enroll your kids in a hybrid program such as landers, ohr hachaim, ner yisroel, or shaar yashuv where you get the best of both worlds.
this will teach the kids a sense of achrayus which is lacking in many yeshivos. btw im not sure why online makes it worse – this kind of stuff was happening before the internet became as prevelant, then it was movies, going places etc.