Q. What were the names of the Nazgûl?
A. The only known text to name any of the Nazgûl is "The Hunt for the Ring" in Unfinished Tales. It names "the second to the Chief, Khamul the Shadow of the East" as Sauron's lieutenant in Dol Guldur; in a previous draft, he was called "the Second Chief (the Black Easterling)". Some believe that Gothmog, the lieutenant of Morgul, was also a Nazgûl; see question III.B.13 for further discussion.
Some people have used the name "Angmar" to refer to the Witch King. We know of no instance in which Tolkien used "Angmar" as a personal name; in his writings it always refers to the Witch King's country. Some still defend the use of "Angmar" as a convenient nickname, but as others find this irritating it is probably best avoided.
Q. Why didn't Sauron use the same Nine Rings to make more Nazgûl?
A. Probably because he didn't need to. Sauron did not lack for servants. The rulers of Rhûn and the Harad were already tributary to him. The benefit of handing out the Nine Rings originally was not so much in creating nine Ringwraiths as in gaining the allegiance of the leaders he corrupted.
It's at least questionable whether any new Ringwraith would have been under Sauron's domination via the Ring mechanism. While a Man who wore a Ring would eventually become a wraith, he would be a slave to that Ring. In the Second Age when Sauron made the original Ringwraiths, he could dominate their Rings with the One, and therefore dominate the bearers of the Nine as well. But in the Third Age, Sauron no longer had the one. The existing Nazgûl were tied to Sauron not by the One Ring but by the Nine, which Sauron held. [L #246 (331)] That raises the possibility that if Sauron gave one of the Nine Rings to another man, he would not only not get control of that Man but actually lose control of the Ringwraith who had formerly worn that Ring!
Conrad Dunkerson pointed out [r.a.b.t article, 15 Feb 2002...] that Sauron could probably dominate the Nazgûl even without using the One. He suggests a different reason why Sauron couldn't make "Nazgûl armies": "Just as any being truly mastering the One would have caused Sauron's dissolution precisely the same as if it had been destroyed, so too would any human mastering (and thus being mastered by) one of the Nine cause its power to be taken from any previous Nazgûl just as if the Ring had been destroyed [or] rendered powerless."
Hope this helps.