You ask two questions:
- Why are the authors of the first four books of the NT called, "Evangelists?"
- Why do we see a shift away from using that title recently?
In answering the first question we need to look at the manuscripts as they are handed down to us. In the earliest manuscripts there were titles, mostly at the beginning (though sometimes concluding and at the end) that gave us details about the author. Take, for example P66:
Notice the title at the top. It reads:
([The] gospel according to John.)
This title was not part of the original text. The original text just simply started with the content of what John was handing down to us:
(In the beginning was the word...)
These titles were added fairly early to help the reader. There are two details to take note of in those titles:
- It's the gospel. That comes from two Greek words: ⲉⲩ (good) and ⲁⲛⲅⲉⲗⲗⲓⲟⲛ (announcement). From this word we get the origination of the authors of the first for books of the NT. They are those who share the "good news" with us. And as a result they are then called the "Evangelists."
- We also note that each of these gospels are the gospels "according to" or "in line with" [author]. This is important. These writings didn't come from or belong to the four evangelists. They belonged to Jesus. They were handed down from the Holy Spirit (2Pet. 1:21).
So, in older translations of the Bible (esp. KJV), one finds the full, expanded titles like "The gospel according to Mark." In the most expanded form the KJV even presumptuously tells us who the author of the letter to the Hebrews is (even though that is actually lost to us). The title for that letter just simply says, "ⲡⲣⲟⲥⲉⲃⲣⲁⲓⲟⲩⲥ" (to the Hebrews).
The second question you ask is much related to the first. Why is there this omission of the title "Evangelist" in modern bibles (and the full, expanded, 'gospel according to ')? The simple answer is this: The title is not part of God's canonical, inspired word. It was added later to help the reader. We know who the authors were both because of the content of the gospel itself and because of references by the early church fathers. But the titles, themselves, were added later.
And, to my knowledge, this isn't due to any theological drift or straying emphasis. It's just simply the translators trying to share with us (at least as much as they can) the text itself and not any extra.