(crownedrose here to answer) Fantastic question! It pretty much boils down to the origin of “Tertiary” which was pinned back in the 1700’s by an Italian geologist, Giovanni Ardunio. He had split the Earth’s time into four periods when studying in the Alps: Primitive, Secondary, Tertiary, and the well known Quaternary (the only term to have truly survived/recognised).
When it comes to the term in question, what was once the Tertiary has now been split into the more well known and used terms. You have the Paleogene period (the first in the Cenozoic era), and its three Epochs: Paleocene, Eocene, and Oligocene. Originally the Tertiary was both the Paleogene (aka informal ‘lower Tertiary system’) and Neogene (aka informal ‘upper Tertiary system’) periods, respectively. Because it is not recognised as a formal time unit by the International Commission on Stratigraphy, the change to the Cretaceous-Paleogene (K-Pg) extinction event was imminent.
So when it comes to the change in names, it was all because of the advancement of knowledge, discoveries, and exploration by other geologists and palaeontologists with much more detailed and accurate research from all over the planet. Ardunio’s work (and four names) had only been explored in the Alps where he researched, so when they were applied to other areas outside the Alps, that’s when the terms (Primitive, Secondary, and for the most part - Tertiary) had to be dropped; because - well - everywhere on the planet is not exactly like the Alps! To sum all of this up (it’s ridiculously late where I am so I apologise for the rambling, and hopefully this has all been making sense), the name was changed to be up-to-date with the recognised time units we have now. Most people (including myself), still refer to it as the K-T extinction event, but with time we’ll all probably get used to its new name.