The New Testament gospels were all written anonymously. During the second century, the Church Fathers attributed each of the gospels to the apostle they thought most likely to have written each, attributing to the disciples Matthew and John the gospels that now bear their names. However, biblical scholars say that the gospels could not have been written by eyewitnesses to the events portrayed. We do not know who the authors really were.
Another Answer:Yes. Though they do not name themselves, a close read of each Gospel holds enough clues to fully suggest they wrote each of their works as modern scholars who comprise the New King James Study Bible, etals, agree. Hence this basic assumption has been consistent since the early centuries A.D..