Tofu brain is pickled with "gypsum", and the solidified soybean milk is fresh and tender, which is quite similar to the "brain pulp" of glistening, which is probably why it is called "tofu brain".
Old tofu is marinated with "brine" (the brine block formed by magnesium chloride crystallization is a commonly used coagulant for making tofu). After solidification, the texture is old and tough, quite like tofu, so it is called "old tofu"