They are not "Western European" names per se, instead these names are common in Western Europe, America, etc. specifically because they spread along with Christianity.
Names are transliterated because of a desire to keep these words as close to the original as possible, but there are differences between languages, such as how words are used and what letters and sounds are available. The nature of these changes is fairly consistent for words outside of the Bible writings which are transliterated.
The exact nature of these transliterations are a better discussion for a linguist group, but I will give some simple examples to help explain how we use the literal words from the translations.
Take Mark, for instance. The original word is "Μάρκος" in Greek. That's actually what they called him. That's the actual letters they wrote in the original manuscripts. At least, that's a digital representation of the Greek phenoms which were written down by people who knew him. The originals were probably all upper case with no spaces or punctuation. All of these letters have a a very consistent transliteration into Roman characters (which is what English uses), and even the letters look a lot like the original Greek letters. In that sense, you could spell it in roman characters as "Markos". But in Greek, the last to letters, the "ος" are part of the word that marks it's place in the sentence. In this instance, it's in the singular nomitive case. You might also see it as "Μάρκον", "Μάρκου", and so fourth, depending on where it is in each sentence. In English, we don't have any need for that ending because we determine part of speech by location in the sentence. So, we simply drop that changeable part, and that leaves us with "Mark". It's literally the English way to write the word that appears in the manuscripts. The same is true for many other names.
Some transliterations aren't as obvious. Of most interest is "Jesus". In Greek, that is "Ἰησοῦς". To a casual observer, it's hard to see the connection here. However, to a Greek student, it is obvious. The "σ" and "ς" are both the same letter, and is the only Greek letter which changes grapheme by location. It relates to the roman "s". The "η" is a little hard to transliterate into roman letters. That transliterates as "e", though it technically has more of a vowel sound like "hey", which is different than epsilon, also transliterated as "e". The "Ἰ" is an "iy" like sound, explicitly without aspiration. So, you might think it should be transliterated as "I". However, the Greek had no "J" character or sound, and the "Ἰ" was as close as they could come for words that had "J" like sound. So, if the Greek Jews were trying to write something like "John" or "Joshua", they would have had to use "Ἰ" instead. It is very common when transliterating Greek words, especially those which may have been based on Hebrew words, to transliterate "Ἰ" to "J". That leaves the "οῦς". Once again, in the Greek, the ending can change based on part of speech, but this form is a bit different. The "οῦ" is a dipthong which doesn't quite have a good one to one relationship with roman letters. Even though you could probably get away with "ou", it has been very common to tranliterate "οῦ" as "u" in English. That leaves us with "Jesus".
As for "Yeshua", that comes from a transliteration of the Hewbrew. As to which is preferred there, between the Greek or the Hebrew, that can be a very different matter. But neither is arbitrary. That may be a good question for another time.
Sometimes, the name can be transliterated differently into roman characters but different languages. One example is "Πέτρος". A close transliteration of the characters might be "Petros", and it's basically the Greek word for a stone. The "ος", as stated before could be dropped for English. And English likes "er" better for the "r". Spanish, on the other hand, doesn't like the "t" in favor of a "d". In English, it becomes "Peter", and in Spanish it becomes "Pedro". Both are very popular names in their respective languages in regions where Christianity has spread.
We do see "Saul" and "Barnabas" in the Bible. And when that's what is used in the Greek text, that's what's used in at least the KJV and probably most other formal equivalent translations. One exception to this rule may be "Calvary" and "Easter", which in the KJV may be dynamic equivalent variants rather than simple transliteration. However, to my knowledge, all of the names of people were simply transliterated. The Bible authors themselves, under inspiration of God, chose which names they wanted to use. The translators just copied that. If you are asking why Peter is sometimes called Simon and sometimes Cephas, etc. by the original authors, that's a good question, but a different question. The reasons would likely be different for each person and each instance. Each author (Paul, Luke, etc.) may have different reasons, such as target audience, or they are quoting a person speaking, or even to emphasize a new name, etc.
The names you mentioned were common Greek names, not Anglo-Saxon names. These names became popular because they were in the Bible and as the Bible spread, particularly throughout Western Europe and the Americas, people named their children after the famous names in the Bible. Some names were more famous, like Mark, and Peter, and John. Some names just didn't get mentioned as much and weren't as famous, like Dorcus or Barnabas. Sometimes, people still do pick out the lesser common names. But the more popular the person or name is in the Bible, generally the more likely that people will use that name.
The same thing is true of Hebrew names, too, like Daniel, Jonathan, David, etc., which break down into Hebrew words. Those Hebrew words, just like the Greek words, spread into English and other languages because of the spread of the Bible.