Albert Barnes Commentary 2 Thessalonians 3:14

"And if any man obeyeth not our word by this epistle, note that man, that ye have no company with him, to the end that he may be ashamed." — 2 Thessalonians 3:14 (ASV)

And if any man does not obey our word by this epistle, Margin, or signify that man by an epistle. According to the marginal reading this would mean, "signify, mark out, or designate that man to me by an epistle." The difference is merely whether we connect the words "by the epistle" with what precedes, or what follows. The Greek would allow either construction (Winer, p. 93), but it seems to me that the construction in the text is the correct one, for:

1. the requirement was to proceed to discipline such a man by withdrawing from him;
2. in order to do this it was not necessary that the case should be made known to Paul, for there was no conceivable difficulty in it, and the effect would be only unnecessary delay;
3. Paul regarded the right of discipline as residing in the church itself, and did not require that cases should be referred to him to determine (see Barnes on 1 Corinthians 5:2; 1 Corinthians 5:3; 1 Corinthians 5:4).
4. Though the Greek will allow either construction, yet it rather favors this (see Olshausen, in loc.).

Note that man. The word here used means to mark; to sign; to note with marks; and the idea is, set such a mark upon him that he will be shunned; that is, withdraw all Christian fellowship from him.

And have no company with him. The Greek word here means, to mix up together; then to mingle together with; to associate with. The idea is, that they were not to mingle with him as a Christian brother, or as one of their own number. They were not to show that they regarded him as a worthy member of the church, or as having a claim to its privileges. The extent of their discipline was, that they were to withdraw from him (see Barnes on 2 Thessalonians 3:6; Matthew 18:17).

Compare 2 John 1:10–11.