I do think that Cassie should take on the name Fury. It fits with her appearance - she looks a LOT like the original Fury - and she doesn't exactly have a name that she can just use for iconicity's sake like Donna Troy does (and even then, Donna and Artemis are both said to be other Wonder Women). I think her origin as it is would be fine, but I don't think she should get her own lasso. Maybe give her something that's more explicitly like a whip? The lasso is Diana and Donna's thing, especially Diana's, to the point that Yara doesn't have a lasso but has something similar that is based in Brazilian myth.
As far as designs go I think I'd keep her with the red color scheme (since Donna seems to have entirely taken on the Troia Black/Silver even if they keep going back to red and gold) and go with something like this:
Very modern, very athletic, very casual which is something that I feel like Cassie should represent. I also think that she should struggle with a little bit of rage issues like she did under Johns, and it would be in part to reference her new codename. I also like the idea of her using lightning as part of her skillset, but wouldn't make her electrokinetic. Instead I'd give her one of Zeus' thunderbolts, which she can use like a lance or javelin.