Curate, connect, and discover
So we all know that Tom's nickname name translates to "flight of death" in French.
Which is ironic because he fancied himself immortal, having made his Horcruxes. And it was a nickname he received/made not long after Hogwarts, i.e. not long after he made his first Horcrux and believed himself immortal (He just didn't use it openly until a decade later).
So little Tom was doodling with his name, trying to make something that was in no way reminding of his Muggle heritage, and also remembering the French he glanced at when he learned that it was sort of a "pure-blood" language tradition.
And little Tom, believing himself to be newly immortal, stumbles upon an anagram , a smush of vol-de-mort that means death flies. He sees it as fate, that death flies from him because he is just that powerful as a student.
And he needs to be seen as noble, that he is descended from pure blood, that as a descendant of Slytherin he is the true lord of darkness.
And thus, the name Lord Voldemort was born.
I think that a lot of people forget that Salazar Slytherin wasn't racist.
And no, before you go all crazy on me just remember in the second book, when fear and anger and all kinds of emotions were running wild and everyone distrusted Slytherin House, students asked a teacher about what happened. And that teacher, a ghost who for all we know could have been there when it actually happened, gave an honest answer.
"Slytherin wished to be more selective about the students admitted to Hogwarts. He believed that magical learning should be kept within all-magic families. He disliked taking students of Muggle parentage, believing them to be untrustworthy."
Look at the language. Look at it, and understand that Salazar didn't see Muggle-borns as inferior, as worse. He saw them as untrustworthy.
Why, you ask? Well Professor Binns answers that as well!
"[The founders] built this castle together, far from prying Muggle eyes, for it was an age when magic was feared by common people, and witches and wizard suffered much persecution."
Salazar didn't like Muggles because they were hunting his family, his people, and persecuting them with horrific violence. He didn't trust Muggle-borns because how could he know that they wouldn't betray the magical world and tell their families that the kid two villages over practices magic with him on Tuesdays?
And yes, witches and wizards had ways to make it look like they burned at the stake when they actually survived, such as the Flame-Freezing Charm. But young children, with little control over their magic? If they were caught or exposed, well, it probably wouldn't end well for them.
Plus, wizardkind is outnumbered by Muggles, by a huge amount. If a village of Muggles who hated and feared magic discovered that a family of wizards and witches was among them, the parents would be burdened with trying to flee from a few hundred people while protecting their kids (who can't control their magic).
Salazar Slytherin didn't like Muggles or Muggle-borns. He hated them and feared them, not because they were inferior, but because they were dangerous. And while murdering children with a giant snake is not a good way to solve this danger to his family, people, and culture, it HAS to be seen that his actions were born not from arrogance, but from fear.
And there were Slytherins who knew this, long before Muggles had become so othered from wizarding society that some families started to believe that Muggles were inferior to those with "pure blood." Like Merlin, Prince of Enchanters, arguably the greatest wizard of all time, who founded the Order of Merlin to protect and aid Muggles, whose name has become synonymous with Muggle rights activisim. Merlin, a Slytherin.
If Salazar Slytherin was alive in the 20th century, he would laugh at the idea that Muggles were inferior. He would be the first to point out that Lily Evans and Hermione Granger, the brightest witches of their age, were Muggle-born. He would scorn the idea that pure-bloods were better, saying if that's true, why is Draco Malfoy, a pure-blood, second to a Muggle-born?
Salazar had questionable morals, to be sure (anyone who doesn't think so can re-read the Chamber of Secrets, where he hid a giant snake in a school full of children to murder the ones he deemed dangerous). But he never, never once thought that Muggles were inferior to wizards.