|10th century Byzantine illustration of Luke the Evangelist.|
Here are his comments regarding the identity of Theophilus (it can be viewed at its original source here):
"Within five years or so of Jesus’ death, a Jew named Theophilus was appointed High Priest by Vitellius, who was Prefect of Judaea from AD 35 to 39 (Emil Schürer, A History of the Jewish People in the Age of Jesus Christ, rev. ed., 2:230). Nevertheless, in light of the thoroughly Greek cast of Luke’s Gospel and book of Acts, it is safe to see the Theophilus whom Luke addresses as an educated Roman official (Luke 1:3; Acts 1:1). This observation is made more secure by the fact that the term translated “most excellent” in Luke 1:3 is applied to ranking Roman officials in more or less august situations in Acts 23:26, 24:3, and 26:25. In a different vein, in my opinion, it will not do to argue that the name Theophilus simply bears the meaning “friend of God” or the like, thus shedding it of any tie to the world of living Roman officials. An addition in the Joseph Smith Translation seemingly stands against this sort of reading of the name, making the name very personal in an interesting add-on to the text (see JST Luke 3:19)."
Here is the JST translation of Luke 3:19-20 that he refers to:
19 For it is well known unto you, Theophilus, that after the manner of the Jews, and according to the custom of their law in receiving money into the treasury, that out of the abundance which was received, was appointed unto the poor, every man his portion;
20 And after this manner did the publicans also, wherefore John said unto them, Exact no more than that which is appointed you.