Robin Lane Fox provides an interesting take on the addressee of Luke and Acts:
Acts and its companion volume, the third Gospel, were dedicated to “most excellent” Theophilus, who wished to “know more exactly” about the faith “of which he had heard.” Only one other type of person is called “most excellent” in the two books: a Roman provincial governor. The usage of contemporary Emperors and the incidence of the title in inscriptions and the papyri confirm that “most excellent” people were people of very considerable rank and position: Theophilus, then, is the cover name for a highly placed figure in Roman circles. Acts’ abrupt ending is explained if “Theophilus” knew the sequel to Paul’s years of arrest. “Theophilus” had heard of Paul’s trial and execution: perhaps he had attended both. He wished to know the truth of a faith which had interested him but now lay under this recent cloud. Acts and the third Gospel are the first, and greatest, of Christian apologies to be addressed to highly placed pagans.