Who were the Ringwraiths?

[Aiwendil]

Gothmog was a commander of the armies of Mordor, but was he a nazgul?
I don't think so. (But I don't know what was he then...)

This is both unknown and unknowable. The only "evidence" that he was a Nazgul is the line of reasoning:

1. After the Witch-king's death, the second in command of the army would have taken over.

2. The second in command must have been the second most important member of Sauron's forces present at the battle.

3. The Nazgul were present and are more important than any other of Sauron's minions.

4. Therefore Gothmog is a Nazgul.

This line of thought does actually make some sense, but it's certainly not airtight. And that is that. I'm afraid there's even less room for a well-argued position here than in the Balrog wing debate.