How many different supranyms has Kang the Conqueror used?
That we know of? Eight. (With a big asterisk on a couple of those.)
(an artist's rendering of Kang the Conqueror and his various other costumed identities)
Nathaniel Richards was born in the 30th century A.D., purportedly a descendant of either Reed Richards of Victor von Doom. By way of a time machine, Richards traveled back in time with the intention of conquering other time periods, arriving first in OId Kingdom Egypt, where he ruled as Pharaoh Rama-Tut.
(artist's rendition of Richards as Rama-Tut, based on the recollections of the Fantastic Four)
There, Richards remained until he was deposed by the Fantastic Four on a time-travelling adventure, and forced to return to his home time period. Or, he would have had he not encountered a temporal anomaly.
This anomaly stranded him in the early 21st century, where he came into conflict with the nascent Avengers as the Scarlet Centurion, a guise seemingly inspired by that of Doctor Doom. The Centurion was defeated and sent packing by the Avengers, specifically thanks to Hank Pym's ingenuity.
And here is where things get messy.
In one timeline, Richards became Rama-Tut once more, and returned to the future - aiming for his native 30th century but arriving further down the timeline thanks to the same temporal anomaly that landed him in the 21st. We'll come back to that one.
But in another, Richards remained the Scarlet Centurion, and returned to a different future timeline. This Richards would come to be a regular menace of that timeline's modern-day heroes, the Squadron Supreme. (Details on this are sparse; the Squadron were notoriously tight-lipped about most of their past exploits during their stay in this reality.)
Back to the "main" Richards, upon arriving in the future time he'd landed in, he began to amass an army, using the advanced technology of the time period to become what he's best known as to the citizens of this day and age: Kang the Conqueror.
(the cover of Marvel's officially licensed Avengers comic book, volume 3, issue 49; featuring Kang impaling the Earth on the end of the sword-shaped Damocles Base)
Richards, as Kang, or other versions of him from slightly divergent timelines, have attempted to conquer our modern-day Earth on many occasions, each time repelled by the Avengers and Earth's other superheroes. Why he continues to attempt conquest of this particular era is unknown - speculation is that he views it as a challenge to be solved, thanks to the opposition of Earth's superhuman population.
Perhaps the most notable of these occasions was what was referred to as the "Kang War" - Earth's darkest hour and a time when Richards got incredibly close to achieving his goals. Only because of the courage of the Avengers - with the aid of the cult group known as the Triune Understanding - were Kang's forces repelled and the Conqueror himself defeated, though it was a pyrrhic victory in the end. Washington D.C. and other world cities remained in ruins, and the loss of life was astronomical.
(And that's not to mention the genocidal attack on Genosha in the midst of all of this...)
At some point during all of the conquering, though, two more major divergences occurred:
A divergent Kang decided to establish a beachhead in the early 20th century and adopted the identity of small-town Wisconsin mayor "Victor Timely" and of Timely's son and grandson as the years passed.
(early 1900s newspaper photo of Victor Timely Sr., colorized)
Kang, as Victor Timely Jr, ironically was instrumental in the start of the first age of superheroes, taking Phineas T. Horton into his employ, and providing him with the laboratory and materials he used to construct the original Human Torch.
2. Another divergent Kang grew tired of conquering and endless war, and traveled to the place outside of time called Limbo, where he aged into the self-proclaimed "gardener of time" known as Immortus.
(photo of Immortus (left) officiating the dual wedding of Mantis to the Cotati duplicate of the Swordsman, and of the Vision to the Scarlet Witch)
Little is known of Richards as Immortus - he seems to prefer a subtle hand to direct conflict with Earth's heroes, appearing in the modern day from time to time to manipulate the Avengers into achieving his goals for him, with a seeming special interest in the Scarlet Witch.
What we do know of Immortus's grander plans come from a single incident known as the "Destiny War" - in which Avengers from across the team's history, including the Wasp and Hank Pym from the then-present, were recruited into a war between Immortus and Kang, who seemed hell-bent on defying his fate. According to the Wasp, it was revealed there that Immortus had been manipulating the Avengers for his own ends through their entire history, starting with their first encounter with the beings known as Space Phantoms.
Another divergent Kang ended up in the 21st century and became a corporate tycoon, the enigmatic CEO of Qeng Enterprises, "Mister Gryphon." Gryphon's true identity was revealed by the Avengers, and he was returned to the timestream to become Kang once more.
And finally, for the last two known versions of Nathaniel Richards, we have to go all the way back to the beginning.
(Avengers file photo of Nathaniel Richards as Iron Lad.)
One version of Nathaniel Richards, as a teenager, was aghast at what his future self would end up doing, and devised an armor similar to Iron Man's. This Richards traveled back to the 21st century and became Iron Lad to atone for his future self's crimes, gathering the legacies of other Avengers to form the Young Avengers.
Eventually, however, this Richards returned to the future after suffering personal tragedy, and followed the destiny of his other selves, becoming Kid Immortus for a time before presumably becoming Rama-Tut.
And so the cycle continues, all roads seemingly leading to Kang.
And now I'm going to have to go take some aspirin, because time travel always gives me a headache. (And seeing your next question in the queue... yeah, might want to keep that pill bottle handy.)