Could Pac-Man eat the Ghost of Christmas Past?

A ring wraith from "Lord of the Rings"

I don't think that those are actually ghosts.

Nine he gave to Mortal Men, proud and great, and so ensnared them. Long ago they fell under the dominion of the One, and they became Ringwraiths, shadows under his great Shadow, his most terrible servants.

https://scifi.stackexchange.com/questions/233663/in-the-lord-of-the-rings-are-the-ringwraiths-really-alive

The Nazgûl are quite the enigma in Tolkien's Legendarium. They are spoken about in a multitude of ways and things are kept rather ambiguous. A few things are however clear. The Nazgûl have not died, meaning they hadn't followed the path of Men who die (separation of fëa from hröa and the spirit going to the Halls of Mandos before departing from the circles of the world). The clearest description is that they had faded:

A mortal, Frodo, who keeps one of the Great Rings, does not die, but he does not grow or obtain more life, he merely continues, until at last every minute is a weariness. And if he often uses the Ring to make himself invisible, he fades: he becomes in the end invisible permanently, and walks in the twilight under the eye of the dark power that rules the Rings. Yes, sooner or later — later, if he is strong or well-meaning to begin with, but neither strength nor good purpose will last — sooner or later the dark power will devour him.
The Fellowship of the Ring, Book 1, Chapter 2: The Shadow of the Past

The Nazgûl were no longer fully incarnate. The physical body of the Nazgûl no longer existed in any form that could be perceived by Mortals. Their lives had been stretched so thin — or as Bilbo put it, butter over so much bread — that their presence in the physical world had all but vanished existing only when clothed by their Master. While clothed they have form in the physical sense, which can be perceived but not seen by mortals. They can speak, smell, see, ride, etc. but as soon as they are uncloaked they become invisible to most, bar those who have a presence in the unseen realm, the "other side", such as Galadriel, Gandalf or Frodo while wearing the Ring.

The use of the word wraith seems to have caused confusion, being deemed to mean that they must be dead; however, the word wraith can also mean an immaterial or spectral appearance of a living being (OED), or a wisp or faint trace of something. However, its use along with other terms such as undead is the cause of significant confusion. The Nazgûl are not like the dead men of Dunharrow, or the barrow wights, for they have not died and weren't just spirits like the other two, unhoused but unable to leave for the Halls of Mandos. The Nazgûl retained some form of physicality or flesh:

So passed the sword of the Barrow-downs, work of Westernesse. But glad would he have been to know its fate who wrought it slowly long ago in the North-kingdom when the Dúnedain were young, and chief among their foes was the dread realm of Angmar and its sorcerer king. No other blade, not though mightier hands had wielded it, would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
The Return of the King - Book 5 - Chapter 6 - The Battle of Pelennor Fields

The physicality of the Nazgûl seems to be heavily dependent on the spells that kept the hidden fibres of their body attached to their will. This alongside the cloaks Sauron clothed them in seemed to allow them to have a presence and interact with the physical world, without which they would be hidden to all but those on the other side.

Finally we look at a word from Tolkien on the longevity of creatures and the lure of Sauron. Through "counterfeit 'immortality'" Sauron was able to trick Men into become the wraiths that were his chief servants. The description as their lives being long or a feigned immortality suggest again that they hadn't died and had their spirit unhoused, they were still attached to their mortal flesh it had just degraded to an unrecognisable artefact.

Longevity or counterfeit 'immortality' (true immortality is beyond Eä) is the chief bait of Sauron — it leads the small to a Gollum, and the great to a Ringwraith.
Letters 286

As for why he's called the Necromancer, that is covered by an excellent answer to this question: Why is Sauron called "the Necromancer"?