The issue is of a writing seeming to bear a claim to have been written by a given author but commonly understood to have been written by someone else. This practise was not uncommon in antiquity. An apocalyptic writing, for example, might bear the name of some great individual from the past, such as Moses. It is not known if the original readers of such a writing would have taken is as having come from the hand of the stated author. Such pseudonymity occurred in Greek, Roman, Jewish and Christian writings.
Among Jews and Christians, pseudepigraphic letters are very rare. For Jews, the absence of any epistolary writing in the OT gave no authoritative precedent to follow. As for Christians, 2 Thess 2:2 suggests that pseudonymous letters were not unknown, but also shows that the apostle does not regard the practise as acceptable (cf. 2 Thess 3:17). Some scholars give the impression that pseudonymous letter-writing was common amongst early Christians, and, moreover, that their readers would recognise the genre and would be aware that the writings did not come from, say, Paul or Peter. But the evidence is that Christians produced few pseudonymous letters (M.R. James cites just six, and these mostly date from the 4th-13th century). There were gospels and acts, but few letters; and there is not one known pseudonymous Christian letter from anywhere near NT times.
The early Christians do not seemed to have been concerned to attach famous names to their writings. Many NT books do not bear the names of their writers (all four Gospels, Acts, Hebrews, 1 John, etc).
One comparatively early pseudonymous letter is referred to in the apocryphal Acts of Paul (cAD 160). This letter was supopsed to have been written by Paul to the church at Corinth (‘3 Corinthians’). The letter was so highly esteemed that it was for a time included in the canon of the Syrian and Armenian churches, evidently on the supposition that Paul was the genuine author. Elswhere, however, it was recognised to be pseudonymous, and for that reason excluded from the canon, notwithstanding its edifying contents. Tertullian speaks of writings ‘which wrongly go under Paul’s name’, and reports that ‘the presbyter who composed that writing, as if he were augmenting Paul’s fame from his own store, after being convicted, and confessing that he had done it from love of Paul, was removed from his office.’
The Muratorian Canon mentions a letter to the Laodiceans (evidently composed to fill the gap left by the loss of the letter referred to in Col 4:14) and one to the Alexandrians, ‘both forged in Paul’s name’, and rejected from the canon on that account.
Towards the end of the 2nd century Seraption, bishop of Antioch, forbad the use of a book purporting to come from the hand of Peter, saying, ‘For out part, brethren, we receive both Peter and the other apostles as Christ, but the writings which falsely bear their names we reject, as men of experience, knowing that such were not handed down to us.’ Here again (though the case refers to a false gospel, not a false epistle, a sharp distinction is made between the writings of the apostles and those ‘falsely bear their names’.
There is, then, no evidence that a New Testament Christian could write something in the name of an apostle and expect the writing to be welcomed. There is no evidence to support the opinion of, for example, P.N. Harrison, to the effect that the pseudo-Paul who wrote the Pastorals ‘was no conscious of misrepresenting the Apostle in any way; he was not consciously deceiving anybody; it is not, indeed, necessary to suppose that he did deceive anybody. It is far more preferable that those to whom, in the first instance, he showed the result of his efforts, must have been perfectly well aware of what he had done.’
With regard to the Pastoral epistles, there is the added point that they contain warnings about deceivers, 1 Tim 4:1; 2 Tim 3:13; Tit 1:10 (cf Tit 3:3; 1 Tim 2:7).
The early church was considerably exercised over questions of canonicity, and the issue of authorship was of major concern. In the case of 2 Peter, for example, there question was whether the book was written by Peter: if it was, then it was accepted, if was not, then it was rejected. There is no known example of anyone accepting a book as canonical while denying that it was written by the person whose names it bears. Eusebius, for example, was prepared to accept the Revelation as canonical if it could be shown that the author was the apostle John, but was prepared to wholeheartedly rejected if it was not apostolic.
See Carson, et al, An Introduction to the New Testament, 367-371.