Of the Rings of Power

[Legolas]

In RotK, during the Battle of the Pelennor Fields, after the Witchking was slain, his lieutenant, called Khamul, took up the command of the army. Some people think that Khamul was another Ringwraith, but I personally think that he was just another Orc-Lord. Sauron wouldn't need more than one Ringwraith, when the WitchKing was enough to break down the gates of Minas Tirith.

No. "Gothmog" was the Lt. of Minas Morgul and *might* be a Nazgul (though I don't believe so - search for 'Gothmog' to find conversations about that).

Khamûl was definitely a wraith - second in command to the Witch-King and the Lt. of Dol Guldur. Read these quotes. The first is Christopher Tolkien in the introduction; the second is from IV 'Hunt for the Ring' where Khamûl's wraiths of Dol Guldur meet the Witch-King's wraiths of Minas Morgul.

Unfinished Tales:

But whatever view may be taken of this question, for some, as for myself, there is a value greater than the mere uncovering of curious detail in learning that [...] the Black Rider whom the Hobbits saw in the foggy darkness on the far side of Bucklebury Ferry was Khamûl, chief of the Ringwraiths of Dol Guldur

Therefore when Osgiliath was taken and the bridge broken Sauron stayed the assault, and the Nazgûl were ordered to begin the search for the Ring. But Sauron did not underesteem the powers and vigilance of the Wise, and the Nazgûl were commanded to act as secretly as they could. Now at that time the Chieftain of the Ringwraiths dwelt in Minas Morgul with six companions, while the second to the Chief, Khamûl the Shadow of the East, abode in Dol Guldur as Sauron's lieutenant, with one other as his messenger.

CT confirms the passing reference from the introduction later on:

and it reappears in detailed notes on the movement of the Black Riders in the Shire: thus of the Rider (who was in fact Khamûl of Dol Guldur, see note 1) seen on the far side of Bucklebury Ferry just after the Hobbits had crossed (The Fellowship of the Ring I 5)

Therefore he [Witch-King] sent some of the Riders into the Shire, with orders to disperse while traversing it; and of these Khamûl was to find Hobbiton (see note 1), where "Baggins" lived, according to Saruman's papers.

[note 1] and it may be noted that in a rejected version of the present passage there was only one Nazgûl in Dol Guldur (not named as Khamûl, but referred to as "the Second Chief (the Black Easterling)"), while one remained with Sauron as his chief messenger.– From notes counting in detail the movements of the Black Riders in the Shire it emerges that it was Khamûl who came to Hobbiton and spoke to Gaffer Gamgee, who followed the Hobbits along the road to Stock, and who narrowly missed them at the Bucklebury Ferry (see p.360). The Rider who accompanied him, whom he summoned by cries on the ridge above Woodhall, and with whom he visited Farmer Maggot, was "his companion from Dol Guldur." Of Khamûl it is said here that he was the most ready of all the Nazgûl after the Black Captain himself, to perceive the presence of the Ring, but also the one whose power was most confused and diminished by daylight.