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). 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. And 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 some certainty. The Latin names Lucanus, Lucilius and Lucius in turn come from the common Latin verb lucere, meaning to be light, be clear, shine, beam, glow, glitter (says Charlton T. Lewis, Charles Short, A Latin Dictionary). Other words that contain this verb are luce, meaning by day; lucerna, meaning oil lamp. And words that are related to the verb lucere are the familiar lux, lumen, and luna.
The root exists in Greek as well: the word λευκος (leukos) means (1) light, bright, brilliant, of sun light, or (2) of color: white. In the sense of white, the name Luke is related to the Hebrew name Laban, except that the Hebrew root that gave rise to this name never means light-giving. This Greek word for white shows up in words such as λευκαινω (leukainos), meaning to make white, and an enormous array of words like that—from having white blossoms to having white arms or to be with white horses. The noun λυξνος (luchnos) denotes a portable lamp, and the very fair word αμφιλυκη (amphiluke) denotes the morning twilight. In our times this Greek root survives in the word leukemia.
The name Luke means Light or Of Light.