Are there any alternate versions or textual variations, lacking this particular name in at least one of these two chapters (except perhaps in the final verse of chapter six, where its presence or absence is irrelevant to my research) ?
The note to Darius in 6:1 tells you that in the Old Greek his name is Artaxerxes. To his name in 6:2 there is no note.
Here are the first lines of chapter 9 (from this page):
As you can see, there is no note.