I'm not seeing that Cawley's reconstruction is currently any better or any worse than any of the other half dozen competing academic reconstructions. Needs more work.
Ragnar Lodbrok was supposedly the father of the Ivar the Boneless, Halfdan Ragnarsson, and Ubbe who are mentioned in the Anglo-Saxon Chronicle as leaders of the Great Heathen Army.
Without identifying his father, Cawley identifies this same Ivar one of five brothers who were in Ireland, although he says "It is not certain that Ivar recorded in this chronicle was the same person as Ivar King of Dublin."
Then he adds a brother Halfdan, relying on the Anglo-Saxon Chronicle and the Great Heathen Army for the idea that Halfdan and Ivar were brothers, although he says " It is not certain that Halfdan´s brother Ivar was the same person as Ivar who is named above, as the death of the latter is recorded five years earlier."
When I read all of this, what I see is possibilities that don't quite hang together and no real proof.
It seems to me we're looking for a Geni answer by comparing speculative reconstructions.
Halfdan and Ivar were common names. I don't see any reason to combine the two from the Anglo-Saxon Chronicle with the two in Ireland and Northumbria without better evidence than we have. Certainly not on the basis of one particular reconstruction when we know there are others equally as convincing.
And, just briefly, I want to point out that the reason we see so many trees with these same men under different patronymics is that people have looked at the various reconstructions and filled in a patronymic based on the name of a speculative father.
On Geni, we really should be deleting any patronymic that is not supported by primary sources so we don't keep making the mistake of thinking that someone whose profile says he is Ivarsson has been proven to be the son of an Ivar.