Yep. That’s the only reason I’m very strongly against SE Emperor - I don’t mind the makeup or the altered dialogue that much in general - but “offspring of Anakin Skywalker” kills it for me. It makes infinitely more sense for us to learn that name in an intimate moment with Luke and Ben, after Yoda passes and confirms Luke’s greatest fear. It’s a very deep and delicate scene, perfect for us to learn his name. And, of course, if you miss it, Luke says it to Vader in his face later on, also a good moment.
I suppose in the context of the PT, which is what the 2004 SEs were for, it makes more sense for the Emperor to say that than just “Luke Skywalker”, but looking at the OT as a trilogy, that’s a no no.
Almost like George Lucas designed the saga so the prequels are meant to be watched first or something…