A simple majority vote via the nuclear option could be undone just as quickly once things shifted, and from my understanding would never be an option in future if done once. To actually officially change the rules and eliminate the filibuster in a way that isn’t just procedural a two thirds majority is required.
It was created in its current form by the formal adoption of senate rule 22 in 1917, which would explicitly take a two thirds majority to edit or remove and if not removed would leave the filibuster on the books. It’s also worth noting that filibusters were incredibly rare in the 1800s, especially pre civil war, with its use to stall civil rights legislation mainly being a 1940s and later thing.
The procedure to go around rule 22 by rasing a point of order in contradiction to established precedent is commonly called the ‘nuclear option’ by everyone from the media to reformists discussing it, and is recognized as the only likely way short of the two thirds majority needed to amend rule 22 to get around the senate filibuster. I think the name is more than a little grandiose, but it is the commonly accepted name for the procedure.