From 43 USC Ch. 11A: BOARD ON GEOGRAPHIC NAMES:

The Secretary of the Interior, hereinafter called the Secretary, conjointly with the Board on Geographic Names, as hereinafter provided, shall provide for uniformity in geographic nomenclature and orthography throughout the Federal Government. The Secretary may exercise his functions through such officials as he may designate, except that such authority as relates to the final approval or review of actions of the Board on Geographic Names shall be exercised by him, or his Under or Assistant Secretaries. (July 25, 1947, ch. 330, §1, 61 Stat. 456) [Emphasis mine]

The above lays out very clearly that the Board of Geographic Names is a non-independent body, reporting to and operating under the authority of the Board but subordinate to the Secretary of the Interior, who possesses the ultimate authority on executive (not procedural) matters.

The Secretary shall cause such studies and investigations to be made and such records to be kept as may be necessary or desirable in carrying out the purposes of this chapter [...]
(July 25, 1947, ch. 330, §4, 61 Stat. 456.)

The above clearly establishes that the creation and maintenance of records is left to the discretion of the secretary.

The Board, subject to the approval of the Secretary, shall formulate principles, policies, and procedures [...] Action may be taken by the Secretary in any matter wherein the Board does not act within a reasonable time. [...]
(July 25, 1947, ch. 330, §3, 61 Stat. 456.) [Emphasis mine]

The above was referenced in the most recent precedent for this method of directing name changes, and this interpretation has been supported by now three administrations, as Sec. Jewell directed (in a much more polite order than that trumpling's tripe) the board to adopt the name for Mt. Denali. The board has since then repeatedly clarified that to override an executive order, they would need the intervention of congress (particularly during attempts to revert, and the later successful reversion, of the name from Mt. Denali).

Since it's establishment, the BGN has operated under the executive direction of the Secretary of the Interior, who in turn is directed by the Executive Branch. There is no requirement, in the initial act, subsequent revisions or in the organizational bylaws (which interestingly have been changed by the trump admin, but I couldn't find a meaningful difference to the archived copies?) that name changes must be submitted through the board, that changes to GNIS require approval by the board or that there was any procedural reason that what Trump did by having the Sec. Interior order the change was in any way unofficial or, except morally, improper.

I'm sorry, as much as I wish this weren't the case, you're simply wrong. By every measure the US government has established, that is it's official name in the USA.