Ah, well the piece in the link you gave is in fact one of the lunar items spelling out Nebkheperuriah, and is in fact the best example of this name. It's identical to Nebkheperure except that it has a lunar disc, note the crescent under the disc, and not a solar one. So while Tutankhamun did of course have the usual five names, he has this additional name, but it is not in a cartouche so not part of his titularly in a formal way.
As the throne names of both Neferneferuaten and Smenkhkare were Ankhetkheperure and Ankhkheperure respectively, the lunar items cannot have been theirs as these items are cleary a modification of Nebkheperure and no other throne name will match as it can only be read as Neb-kheperu-re or iah.
So the questions remaining being was it normal for a king to have an informal name based on his real throne name, but never placed in a cartouche and never appearing in any form except the items themselves, which would mean a name used within a family setting. Problem here is preservational bias as we only have these type of personal items from Tutankhamun so cannot know if it was peculiar to him, or common. Then there is the issue of why these lunar items were made for him at a younger age, probably before his name change, and did not have the straps lengthened as he grew older, indicating that this "private" throne name may not have been common at all and may be specific to Tutankhamun.
So to me it looks like a specific attempt to tie him to the Moon/Khonsu very early in his reign, possibly before he ruled alone during the about 18 months that Neferneferuaten ruled between the death of Akhenaten and her own, and these lunar items then being cast aside by, or on, his change of name from Tutankhaten to Tutankhamun.
There is though one other piece of evidence regarding kings and the Moon. In KV62 the gold "state chariot" had only solar motifs, there being no chariot with lunar motifs. However, in the tomb of Thutmose IV the remains of a chariot were found that indicated it was a "lunar chariot". So while we usually disregard the Moon when thinking about the AE, they themselves had a different view. The Moon was not of course prominent, but not entirely absent, at least in the later part of the 18th Dynasty.
Edited 2 time(s). Last edit at 10/28/2023 03:28AM by Corvidius.