Were the names Matthew, Mark, Luke and John common names in the time of Jesus? If not, what were their real names and why were they changed?
The names of the authors of the Gospels have been adapted into English from the Greek of the New Testament.1 However, Hebrew and/or Aramaic were likely the mother tongue(s) of three of the evangelists (Matthew, Mark, and John), and their names reflect this background. Luke's name is Greek.
All of these are normal, common names, and there is no reason to think anyone's name was changed for the purpose of assigning him to a Gospel.
Matthew's is a Hebrew name that comes awkwardly into Greek as Μαθθαῖος (Maththaios). When speaking Aramaic or Hebrew, his friends and family likely called him by the Semitic version, מַתִּתְיָ֫הוּ (Mattith-yahu) or several of the available shortned versions thereof (Mattaʾi, Mattiyaʾ, or Mattiyah). These are derived from the Hebrew nātan ("he gave") and mean something like "gift of God". This name and its variants were very common in Hebrew.2
Matthew appears to have also had a second name, Levi (see Mark 2:14, Luke 5:27). Levi (Λευὶ) is, of course, a Hebrew name for one of the twelve tribes: לֵוִי (lēwı̂). It is also a common male name from the OT. Why Matthew had two different Hebrew names and the nature of the relationship between them has been a matter of much scholarly discussion.
Mark (a.k.a. John Mark)
The full Greek names is Ἰοαν(ν)ες Μαρκος (Ioan(n)es Markos). This has two components. Markos is a Greek name (cf. Latin Marcus), one of the most common in both Greek and Latin speaking communities in the Hellenistic period.3
Ioannes is a Greek adaptation of the Hebrew name יוֹחָנָן (yôḥānān, "Yahweh has shown grace"). When speaking Hebrew or Aramaic, it is likely that yōhānān alone was used.4 Among the evangelists' names, only yōhānān ranks among the top six most common male names in Palestine at the time (#5).5
Luke's is a normal Greek name – Λουκας (Loukás) – by which he likely addressed. Luke was a Gentile whose command of Hebrew and/or Aramaic is unknown, but in any case we are not given a Semitic name.
As noted above for Mark's Semitic name, Ioannes is a Greek adaptation of the Hebrew name יוֹחָנָן yôḥānān ("Yahweh has shown grace"). Because this was a common name among Greek-speaking Jews (see above), John is often referred to with the patronymic τοῦ Ζεβεδαίου ("[son] of Zebedee").
1. Of course, the Gospels are technically anonymous. However, the traditional attributions of authorship were clearly identified with particular men who are known to us from within their pages (and Acts).
2. Anchor Yale Bible Dictionary (citation below) finds at least ten mattaniah's, in addition to one or more each: mattatha, mattathiah, mattathias, mattattah, mattenai, matthat (all derived one way or another from "gift" and "yhwh") in the Old Testament and Inter-testamental literature, s.v..
3. Paul J. Achtemeier. "Mark, Gospel of" in Anchor Yale Bible Dictionary, Ed. David Noel Freedman (Random House, 1992), 4:541.
4. Richard Bauckham Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony (Eerdmans, 2006), p 67ff. The author points out that likely many more people than we realize had both Greek and Semitic names, but because only one was generally used in a specific setting, these are often difficult to trace based on the limited texts available.
5. Richard Bauckham, ibid.
Data on Greek-Semitic equivalences are from New International Dictionary of New Testament Theology and Exegesis. Ed. Moises Silva (Zondervan, 2014).