In Stanford Intellectual vitality supplemental essay I’ve mentioned in the conclusion that I hope that in Stanford I will have the opportunity to research something. Is this mention of Stanford specifically bad?
Your question is should you reference the school name of the school to which you are applying?
How could it be? Now, considering that you probably had a max word count, you could have used the space of those eight letters for something else, but, afterall, it is just eight spaces.
As long as you did not blanket copy and paste that essay into another college’s app and ruin your review at that school, no harm done.
You could probably go without mentioning Stanford specifically, because it is a supplemental essay and only being submitted to Stanford. It cannot apply to any other unis