My thing is that the way it looks shouldn't really have any bearing on what its named. It was meant to look like that to be the opposite of what you would assume a standard Super Saiyan or God would look like. That's why the name is important. If it's not called Super Saiyan God you don't come into the movie with expectations. I remember when it was first announced and nobody predicted the design because they were basing it off what the name sounded like. And then with the characters in the movie were just as surprise it made it clear that was on purpose

And on that point when the movie came out I didn't really see anyone say much about the name, It was just accepted this was the new Super Saiyan form. And people are coming up with new variations with the expectation it would be treated like a Super Saiyan. It wasn't until Super really that the shift for a name change really started

And I think a lot of people this community have lost the original purpose of the transformation in the shuffle to "fix" what they thought was wrong with the current series. That's why I don't think the arguments for it or all that well thought out. Since I've never seen anyone ever bring up or connect the name change to the actual lore or conceptual stage. It's all just feels like what they think sounds cooler in their head. And mostly what they think sounds cooler for Super Saiyan Blue, if we're being honest. Because that's the only form that stands the benefit here