From what I can tell in admittedly fairly brief reading, a single member of the family is trying to remove the name, while the rest of the family simply want it distinguished from the other prizes while not objecting to the use of the name per se.
This statement from Peter Nobel[0], the man actively trying to remove the name, presumably sums up the best arguments he had available against using the name, and makes no mention of other family members trying to deny usage.
[0] https://rwer.wordpress.com/2010/10/22/the-nobel-family-disso...
This is the part that makes it a sham. You call it that to give it a legitimacy it doesn't have. The entire thing is a project in giving economics as a field a legitimacy it doesn't have.
>It is a deceptive utilisation of the institution of the Nobel Prize and what it represents.
https://rwer.wordpress.com/2010/10/22/the-nobel-family-disso...
Not to mention one of its awardees, Hayek.
https://www.nobelprize.org/prizes/economic-sciences/1974/hay...
Which is precisely the problem, and the intended effect. It's a propaganda effort.