I have not done research for this kind of buildings before but we have one quite close to here and that is why I know it is a Gradierwerk in german language. German wikipedia names it Gradierwerk as well and Leo translates that to graduation house. In english Wikipedia the name used it graduation tower, as you have already pointed out.

I believe the main reason there is no common english name for such buildings is that most of them are located in Poland and Germany, a few in France (if you have a look at the list in english Wikipedia). So maybe you just stick to the term graduation_tower which at least corresponds to Wikipedia EN.