is it? I checked the dictionary and it doesn't seem like they're doing anything in vain. https://www.merriam-webster.com/dictionary/vain

1. having or showing undue or excessive pride in one's appearance or achievements : conceited

it's literally the opposite of pride. they're using his name to hide something they're ashamed of

2. marked by futility or ineffectualness : unsuccessful, useless vain efforts to escape

also the opposite, they're trying to use his name in an effective manner to solve a problem

3. having no real value : idle, worthless vain pretensions

same as the previous, it would have a worth to them

4. archaic : foolish, silly

again, they're using it for schoolwork, which is educated, not foolish