There's no name which can be guaranteed to identify the Raven King.
There are many names by which he might be called, but none of his known names are unique to him. They used the moniker "the nameless slave" perhaps because they thought it would be unique to him - or at least more likely to be so than "the King", which could as easily have summoned the King of England - because they didn't know about Stephen Black and his destiny.
This is covered in more detail in the source novel:
Mr Norrell sighed. "It is not like summoning any one else. There are difficulties peculiar to any magic involving John Uskglass."
"Well, for one thing we do not know what to call him. Spells of summoning require the magician to be most particular about names. None of the names by which we call John Uskglass were really his own. He was, as the histories tell, stolen away into Faerie, before he could be christened – and so he became the nameless child in the brugh. `The nameless slave' was one of the ways in which he referred to himself. Of course the fairies gave him a name after their own fashion, but he cast that off when he returned to England. As for all his titles – the Raven King, the Black King, the King of the North – these are what other people called him, not what he called himself."
"Yes, yes!" declared Strange, impatiently. "I know all that! But surely John Uskglass was his true name?"
"Oh! By no means. That was the name of a young Norman aristocrat who died, I believe, in the summer of 1097. The King – our John Uskglass – claimed that man as his father, but many people have disputed whether they were really related at all. I do not suppose that this muddle of names and titles is accidental. The King knew that he would always draw the eyes of other magicians to him and so he protected himself from the nuisance of their magic by deliberately confusing their spells."
-- Jonathan Strange & Mr Norrell, p.957
When he comes to Yorkshire to rewrite his book on Vinculus, they manage to identify his location using "John Uskglass":
Cheerfully he reminded Strange that they still had not found a way to name John Uskglass and that this was certain to be a great obstacle in finding him – by magic or any other means.
Strange, with his head propped up on his hands, stared at him gloomily. "Just try John Uskglass," he said.
So Norrell did the magic, naming John Uskglass as the person they sought. He divided the surface of the water into quarters with lines of glittering light. He gave each quarter a name: Heaven, Hell, Earth and Faerie. Instantly a speck of bluish light shone in the quarter that represented Earth.
"There!" said Strange, leaping up triumphantly. "You see, sir! Things are not always as difficult as you suppose."
-- Jonathan Strange & Mr Norrell, p.964-66
But after he goes back to his fairy realm, they have trouble locating him under any name except "the nameless slave" (which, of course, refers to Stephen instead):
At Hurtfew the two magicians had found The Language of Birds – it lay open on the table at the page where the fairy spell was printed. But the problem of finding a name for John Uskglass remained. Norrell sat crouched over the silver dish of water doing location spells. They had already run through all the titles and names they could think of, and the location spell did not recognize a single one. The water in the silver dish remained dark and featureless.
"What of his fairy name?" said Strange.
"That is lost," replied Norrell.
"Did we try the King of the North yet?"
"Oh." Strange thought for a moment and then said, "What was that curious appellation you mentioned before? Something you said he called himself? The nameless something?"
"The nameless slave?"
"Yes. Try that."
Norrell looked very doubtful. But he cast the spell for the nameless slave. Instantly a speck of bluish light appeared. He proceeded and the nameless slave proved to be in Yorkshire – in very much the same place where John Uskglass had appeared before.
"There!" exclaimed Strange, triumphantly. "All our anxiety was quite needless. He is still here."
"But I do not think that is the same person," interrupted Norrell. "It looks different somehow."
"Mr Norrell, do not be fanciful, I beg you! Who else could it be? How many nameless slaves can there possibly be in Yorkshire?"
This was so very reasonable a question that Mr Norrell offered no further objections.
"And now for the magic itself," said Strange.
-- Jonathan Strange & Mr Norrell, p.980
Note those last few lines: Norrell senses intuitively that they've got the wrong man, but the argument that "the nameless slave" surely cannot refer to anyone else is enough to convince him.