With how similar the Entente of both wars are in terms of members, I think its reasonable to assume that the treaties forming the Entente of GWI might even still be in effect, making the Entente of GWII directly descended from that of GWI. At the very least it means the organisational structures will be carried over, so I think its perfectly reasonable for the two to share a name. a "switch to hard-right ideology" doesn't really matter here to me; The CSA was already pretty reactionary in GWI, Britain is still democratic (though far more limited), and Russia is still Tzarist Russia. The only big difference there is France, which regardless still seems to have the same foreign policy goals and commitments as in GWI, compared to the Axis, which is essentially a brand new alliance formed by Germany, since all of their other allies have been destroyed.Only in the sense it was the same countries involved. In the sense of a switch to hard right ideology and goals its very similar
Well again this isnt entirely true if you consider The Destruction,the Superbombs,whole towns being wiped out and other horrors that reared their head in the SCW that were absent or on a much lower scale than that in the GW.Also the fact that Quadruple Alliance which I shorten to Allies in my headcannon didnt change doesnt mean that the name Entente wouldnt change.The Entente lost the GW and it was lead by people and ideologies that the leaders of those same countries in the SGW believe were weak and a failure and lead to defeat.It actually makes perfect sense that they would want to be known by a different name.
Its Radius Powers actually and it doesnt sound goofy at all to me. Its a very clever name using a synonym for Axis and considering the group of people we are talking about its entirely appropriate...
In terms of Entente war aims, the GWII ones really just seem to be a more extreme extension of GWI ones. The CSA still wants border territory and to make the US weak, the Western Entente now wants to dismantle Germany instead of just crippling it, and Russia wants to reclaim slavic land.
The fact that more war crimes occur in GWII than in GWI doesn't change how similar the Entente of both conflicts are. Both wars have fronts in the same places, both alliances have the same countries, The Entente has widely similar war aims, and both alliances are more directly descended from their predecessors than either the otl Allies or Axis. I don't think popular opinion would associate the alliance name with defeat. I don't really see there being an opinion either way on something like that.
To me, Radius/Radial Powers just sounds like something from Equestria at War. It sounds too fantastical, but I can't really put my head on why.