Complex sentence: Organizers could not use the name of "Isang Yun" because the bereaved family would not permit it; they were not convinced that the competition could be maintained to the level of other reputed competitions.
Split into simpler sentences: Organizers could not use the name of "Isang Yun" because the bereaved family did not allow them to. The bereaved were not convinced that the competition could be maintained to the level of other reputed competitions.