They already tried to do that. I think it is mostly pointless. I would like to compare it to the case of John von Neumann.
He was a hungarian-born dude famous for his work in compsci and to some extent maths around the world war 2 era. His work had way more impact on today's IT than anything GNU or open source, simply because he put his effort in much earlier. Almost all relevant hardware uses the Neumann architecture today. Yet, people call him John von Neumann. The family name might be of germanic origin, but the dude is hungarian so his name is Neumann János, end of story. If someone would like to argue that the germanic name requires the 'von', I ask why Nicolas Sarkozy isn't called Sárközy Miklós, because that family name is of hungarian origin.
So, as you might already feel it, names don't really matter. The next argument against me could be that the free-free thing causes confusion. I believe this is irrelevant because the root cause of the confusion is a lack of interest. The vast majority of people, and even a huge portion of people working compsci don't give two fucks about it. The main exceptions being those who have to explain it over and over, and those who align themselves with free software in relation to their political ideology. Sure, I know, it's a part of everyone's everyday lives, the infrastructure runs on it… but so is carbon. I mean, where would we be without carbon molecules, or water? To most people, personally knowing the difference has little impact on their lives, and any serious impact is in the plane of "what if" scenarios.
There is little proof that a world where every layperson is clearly aware of the distinction between libre and free software is worth the effort of making it happen. Most people who believe there is a great world where this is the case know that this is just a minor detail about it, and put their efforts elsewhere.
If you ask me, I'm fine with free as in beer gnu software and John von Neumann (however much the latter annoys me).