The statement “to Ephesus” in Eph 1:1 has been called into question since some early manuscripts[i] do not contain that Ephesus was the specific Church Paul was corresponding too. Some explanations have been offered like it was more of a general letter meant for many churches which I think has some merit, [ii] but I think D.A.Carson has the best explanation for the reason why “to Ephesus” is probably authentic. He writes, “The words in Ephesus do not appear in our earliest manuscripts, but the grammatical construction left suggests that even earlier manuscripts had two place-names.”[iii] He goes on to write that the two places are, …”Hierapolis and Laodicea…but Ephesus and Laodicea (the two ends of the journey Tychicus would have taken) would more easily account for how the letter came to be known as Ephesians.” [iv]
[i] Jones puts forth some of the textual problems in his commentary on the epistle. He writes, “Basil the Great received the Epistle as addressed to the Ephesians, but quoted and commented on ver. 1 so as to show that ἐν Ἐφέσῳ was not in the manuscripts he used, at least not in those of early date. In the Codex Vaticanus and the Codex Sinaiticus the words are written by a later hand. “ The Pulpit Commentary: Ephesians, ed. H. D. M. Spence-Jones (Bellingham, WA: Logos Research Systems, Inc., 2004), iv.
[ii] Walvoord and Zuck come to the conclusion that even though some manuscripts to not contain this phrase, that Paul meant for this letter to include Ephesus. They write, “The words “in Ephesus” are omitted by some early manuscripts…but strong external and internal evidence support their inclusion.” John F. Walvoord, Roy B. Zuck and Dallas Theological Seminary, The Bible Knowledge Commentary : An Exposition of the Scriptures (Wheaton, IL: Victor Books, 1983-), Eph 1:1; NT Historian Craig Kenner thinks that the Church of Ephesus was probably among other churches that this letter was sent too, but Ephesus was the primary church writing, “Many scholars have argued that Ephesians was originally sent to a number of churches, of which Ephesus was only the most prominent. (Thus it would be a “circular letter,” like imperial edicts.) But because all these churches would presumably be in the area around Ephesus, the history of the Ephesian church will help us understand the background to this letter.” Craig S. Keener and InterVarsity Press, The IVP Bible Background Commentary : New Testament (Downers Grove, Ill.: InterVarsity Press, 1993), Eph 1:1.
[iii] D. A. Carson, New Bible Commentary : 21st Century Edition, 4th ed. (Leicester, England; Downers Grove, Ill., USA: Inter-Varsity Press, 1994), Eph 1:1–2.