"Melkórë", "Melko", "Melegor", and "Meleko" are apparently Valarin, (spoken by the ainu) Eldarin, (spoken by the first elves) or Quenya (spoken by our Noldor Elves of Aman) names that Tolkien used in drafts, before he settled on the Quenya "Melkor" translated in the Silmarillion as “He who arises in might". These are likely related to the little used Eldarin (possibly Valarin) name "mbelekôro".
The early elves of Cuiviénen called him "The Hunter" ("Roimë" in Quenya) and "The Dark Rider", ("Moroquen"). There is a non-Silmarillion reference to "Dark Hunter" ("Moroimë") but not in this defining passage:
"if any of the Elves strayed far abroad, alone or few together, they would often vanish, and never return; and the Quendi [elves] said that the Hunter had caught them, and they were afraid. And indeed the most ancient songs of the Elves, of which echoes are remembered still in the West, tell of the shadow-shapes that walked in the hills above Cuiviénen, or would pass suddenly over the stars; and of the dark Rider upon his wild horse that pursued those that wandered to take them and devour them.""The Enemy" and "Great Enemy" are used thru time for the Bad Guy, but also for his chief in Middle-Earth, Sauron. Word lists render these as "Cotumo" and "Altacotumo"
Feanor once calls the mightiest of all the dwellers in Eä "jail-crow of Mandos", but his name-calling doesn't stick until the darkening of Valinor and his father's murder:
"Fëanor rose, and lifting up his hand before Manwë he cursed Melkor, naming him Morgoth, the Black Foe of the World; and by that name only was he known to the Eldar ever after."JRRT considered but set aside "Moriñgotho", "Moringotto" and "Moricotto" for "The Dark Enemy" here. The Sindarin "Bauglir", meaning "The Constrainer" appears the Silmarillion often but only as "Morgoth Bauglir".
Also in Sindarin, the elven language of Middle-Earth, are "Belegûr" for "He who arises in might" and "Belegurth" for "Great Death". "Belcha" is not used in Silmarillion, but others have ascribed it to a Sindarin dictionary. It's clearly not Eldarin nor Quenya nor Valarin, since none of those use an initial letter B.
Humans in later ages added "Dark Lord", "Dark King", "Dark King of Angband", "Black King" and "Lord of the Dark" to our antagonist's monikers.
The Bad Guy even gives himself a few titles. When speaking to Noldor, he calls himself "Vala" also, and "friend to the Noldor". When speaking to to Húrin, he claims "Master of the fates of Arda" (rightly belonging to Námo Mandos) and "Elder King", which was accurate in the brief time the Bad Guy was the only sentient creature in the World, until the arrival of meritous Manwë.
Fittingly, the Bad Guy gets exiled the last paragraph of the Silmarillion (emphases mine):
the Valar thrust [Morgoth himself ] through the Door of Night beyond the Walls of the World, into the Timeless Void; and a guard is set for ever on those walls, and Eärendil keeps watch upon the ramparts of the sky. Yet the lies that Melkor, the mighty and accursed, Morgoth Bauglir, the Power of Terror and of Hate, sowed in the hearts of Elves and Men are a seed that does not die and cannot be destroyed; and ever and anon it sprouts anew, and will bear dark fruit even unto the latest days.
Here ends the SILMARILLION.