I am so sorry that this is happening, and apparently this behaviour can happen in year 8 as students spread their wings. I am aware of something similar to another girl and the parents spoke to the school, but I think at this stage you should go higher, i.e. deputy head as these things can get out of hand if not dealt with swiftly. The school needs to make this clear that this behaviour is not to be tolerated.
At the same time, your DD should keep away from her and find other friends. The key thing to explain to your DD is that the behaviour of this person is not about your DD but about what the perpetrator is feeling about herself. This is not an easy task for a young person, but if she could understand that, it might take the sting out of it.
You did not say how this girl gets in the way of your DD finding new friends as that is quite vile behaviour. Does she have some kind of vendetta with her, or does she just want the other friend to herself?
You might also consider joining your DD to clubs outside of school, so she has another space to be herself and find new friends there.
I wouldn't change classes just yet. Also as hard as this is, this is also a life lesson as I went through something with my DD in y4-5 and it was awful and we thought of moving schools, but she got through it, and it was a lesson learnt - albeit a hard one. Hope this helps.