The name Luke in the Bible
There's only one Luke mentioned in the Bible and that sporadically. Luke is Paul's "fellow worker" (Philemon 1:24) and his (?) beloved physician (Colossians 4:14) and possible last companion (2 Timothy 4:11).
Ancient church traditions attribute the authorship of the third gospel and Acts of the Apostles to this Luke, but there's no evidence for that (apart from the tradition, which obviously didn't rise out of nowhere). The bottom line is that the third gospel isn't signed by anyone and we don't know who wrote it. And the problem with Lucan authorship is that "the difference between the Lucan Paul and the Pauline Paul is not minor" (as the Oxford Companion to the Bible puts it).
Ergo: either Paul's fellow worker Luke had a knack for changing things, or Paul did, or Luke didn't write Acts. One very obvious lesson the reader can learn is that since the Bible doesn't find it important who wrote the third gospel, it probably isn't. But since it's always been called Luke, Luke it is.
Etymology of the name Luke
According to Spiros Zodhiates (Complete Word Study Dictionary), the Greek name Lucas is a contracted form of the Latin name Lucanus or Lucilius — but not of Lucius, Zodhiates adds with bewildering resolve. The Latin names Lucanus, Lucilius and Lucius in turn come from the common Latin verb lucere, meaning to be light or white:
The name Luke means Light or Of Light.