When were the Gospels first attributed to their traditionally attributed authors and why were they attached to the Four Evangelists?

This is actually a great and relatively easy question to answer.

You're right in assuming that the Matthew, Mark, Luke, and John names were all added later since the original letters (or books as we call them now) had no names on them at all. We started seeing names appear around the year 185 CE. The most common reason most historians and Textural Scholars believe this started was because when infighting between rival Christian sects (and there were many of them with varying levels of belief in according to today's Christian Standards) made them question all of each other's doctrine. Bart Ehrman's book, Jesus, Interrupted: Revealing the Hidden Contradictions in the Bible (And Why We Don't Know About Them) discusses this very thing, saying:

These books are called Matthew, Mark, Luke, and John because they were traditionally thought to have been written by Matthew, a disciple who was a tax collector; John, the “Beloved Disciple” mentioned in the Fourth Gospel; Mark, the secretary of the disciple Peter; and Luke, the traveling companion of Paul...

But if Matthew and John were both written by earthly disciples of Jesus, why are they so very different, on all sorts of levels? Why do they contain so many contradictions? Why do they have such fundamentally different views of who Jesus was? (Page 102)

There are several theories for why they picked these names, but the one that I've come to believe is that it has to do with different sects believing that their own doctrine was legitimately written by someone important. By claiming that an apostle, or someone close to an apostle wrote their book, it was therefor likely that they can say, "See, we are legitimate Christians because of who we follow." No doubt other people had similar ideas when they created newer Gospels in the second and third century but wanted theirs to still be viewed as authentic.