A man of the Black Númenórean descent, perhaps.

What would "other" be?

Orc. Four reasons:

1) the only named Black Numenorean in Sauron's service in the TA (so not counting Herumor and Fuinur in SA) is "the Mouth of Sauron". He's basically an unnamed servant of Sauron, because "his name is remembered in no tale, for he himself had forgotten it". He's been so long under the dominion of the Dark Lord that his past identity has been all but erased: greed and cruelty is all that remains, the rest is a shadow of a Man. I think that other high-ranking Black Numenoreans would experience this as well and become a nameless agent, bound to the Dark Lord, rather than assume a new name. The Morgul Lord/Witch-king was also a Numenorean (probably) and similarly lost his identity (sure, different reason, but still). So I don't think a Black Numenorean fits the bill.

2) Orcs seem to keep fresher memory of the Elder Days than the rest of Sauron's servants. For example, in The Hobbit, the Goblins of Goblin-town recognize Thorin's sword as Orcrist, the "Biter" forged for the "Goblin-wars" (=the War of the Jewels) and used in the Fall of Gondolin. Since at least some of them recall that battle, *where Balrogs participated under the original Gothmog, it seems pretty reasonable that a knowledgeable Orc could have taken the moniker Gothmog to evoke the memory of its namesake.

3) Idk he's a Maia, or one of the "Orc-formed Maiar" (Morgoth's Ring)/Boldogs. Firstly, I don't think a Boldog would be subordinate to a Nazgul. Secondly, I don't think Sauron surrounded himself with that many fallen Maiar. Saruman, the "ally, or servant, of Sauron" (UT) was the only lesser Maia under Sauron's sway that we explicitly know of. And how did that turn out? Saruman "cheated [his] new master" (The Two Towers) and tried to claim the Ring for himself... I don't think the Dark Lord would surrround himself with many vassals of this caliber, who could betray him. So I don't think a fallen lesser Maia fits the bill.

4) we don't know if Half-trolls are actual beings or just a descriptive term for some kind of elite brutish warrior from Harad. I heard some people on Reddit who considered that he could be an Olog-hai. As far as I recall, Tolkien merely stated that the Olog-hai were more cunning/smarter *in comparison to regular Trolls. That does not mean that they had the intellect necessary to take some degree of command after the Morgul Lord's death as Gothmog did. So I don't think a Troll/Half-troll/Olog-hai fits the bill.

So yeah, I think that Gothmog, the Lieutenant of Morgul, was an Orc and that PJ made the right choice. But we'll never know 100% for sure - we're not Tolkien.

@Alex of Star Wars While you make several good points, I disagree. While your first statement is sound, "man" is a wide category: Gothmog could be an Easterling or Haradrim.

But the name? There wouldn't be any Haradrim named in the Black Speech. (May be wrong)

^ if they're an important enough officer, they could. We don't know much about Sauron's army hierarchy.

I picture him as a black Númenorian, dk why tho.