The exact meaning of aen in King’s Letter has long been a source of speculation. It is generally thought to be some sort of subjunctive marker (“should”) or other marker of uncertainty, the earliest idea along these lines being Carl Hostetter’s suggestion that it might be related to Q. nai “may it be” (VT31/16). The 2023 publication of the earliest draft of the letter in The Art of the Manuscript provides very strong evidence for this theory. In this earliest draft, the word was first written as ge (AotM/62), likely a mutated form of ce which could be the cognate of Q. cé “maybe” or “if” (VT49/19). This was revised to ain, likely based on primitive ✶ai “supposing” from around this period (PE22/139). This was revised to aen in all later versions of the letter, reflecting the Sindarin sound change whereby ai became ae.
Assuming this analysis is correct, then aen probably means something like “should” or “could” and the untranslated parenthetical comment i sennui Panthael estathar aen means something like “who [rather?] should be called Fullwise”, a play on Sam’s actual name Panthael = “Halfwise”.
Some scholars believe this word to be cognate to Quenya nai "may it be". Other think that it is the pronoun "they". The context in which this word occurs (The so-called "King's Letter") is not clear enough to intepret it with certainty