Bart Ehrman was on the July 18 and July 25 editions of the Unbelievable? radio program with Tim McGrew. They were discussing the reliability of the gospels. During the first program, Ehrman cited Irenaeus as the earliest source to attribute the four gospels to the individuals traditionally thought to have written them. He also said that the gospels are anonymous, that they don't claim to have been written by eyewitnesses, and that the early sources who make authorship attributions for the gospels are Christians who therefore had a Christian bias that makes their attributions suspicious.
There are a lot of problems with Ehrman's claims. I want to provide several examples.
The authors of the gospels could have been identified early on in multiple ways, not just by means of authorship claims within the main text of each document. There could have been document titles, tags attached to the documents, writing on the sides of codices, and oral reports about authorship circulating along with the documents, for example. See here. The idea that none of those means of identifying the author were utilized for any of the four gospels for decades, or that every use of such a means was wrong for decades, is tremendously unlikely. Not only would there have been multiple motivations to identify the author of each document early on in its own context, but there would have been further motivation as soon as two or more gospels were gathered together and used in church services, libraries, and other contexts and, therefore, needed to be distinguished from one another.
And even in their main text, in what sense are the gospels anonymous? The author of the third gospel tells us that he knew Paul and traveled with him and had met James, the brother of Jesus (Acts 21:18). The fourth gospel claims to be written by a close disciple of Jesus and close companion of Peter. Both documents also give us a lot of other information about their authors. What I've cited above are just a few examples. To call such documents "anonymous", without further qualification, is misleading, especially in a context like the one Ehrman was addressing. In that context, we wouldn't need to know the names of the authors of the third and fourth gospels in order for their characteristics discussed above to be highly significant.
Furthermore, if careless or dishonest Christian bias had as much influence on authorship attribution as Ehrman suggests, why did they come up with figures like Matthew, Mark, and Luke? John's the only one who makes much sense as a fabricated author. Martin Hengel, who rejected authorship by the apostle Matthew, nevertheless acknowledged:
"Another comment on the name Matthew: apart from the first Gospel, to which he gives his name, Matthew plays no role in primitive Christianity. He appears only in the lists of apostles. He is only mentioned rather more frequently at a substantially later date in apocryphal writings on the basis of the unique success of the Gospel named after him. That makes it utterly improbable that the name of the apostle was attached to the Gospel only at a secondary stage, in the first decades of the second century, somewhere in the Roman empire, and that this essentially later nomenclature then established itself everywhere without opposition. How could people have arrived at this name for an anonymous Gospel in the second century, and how then would it have gained general recognition?" (The Four Gospels And The One Gospel Of Jesus Christ [Harrisburg, Pennsylvania: Trinity Press International, 2000], 71)
What about Mark? Not only was he a relatively minor figure in early Christian history, but he even had multiple negative characteristics that would have made a false authorship attribution to him highly unlikely. Luke wasn't as bad a candidate for authorship as Mark, but he was a relatively minor figure. Why not choose one of Paul's more prominent companions, like Titus?
McGrew responded to Ehrman's claim about Irenaeus by citing Papias, who named a couple of the gospels' authors several decades earlier than Irenaeus. And Papias cites an earlier source for his information. He doesn't just give us his own view. (On Papias' significance and credibility, see here and here.) For a discussion of other sources who named the gospel authors prior to Irenaeus, including non-Christians, see here. Concerning non-Christian sources in general, regardless of whether they predated Irenaeus, see here and here.
The evidence suggests that men like Ptolemy and Marcion were corroborating the traditional gospel authorship attributions decades before Irenaeus wrote. Justin Martyr doesn't name the gospel authors, but he refers to "the memoirs which I say were drawn up by His apostles and those who followed them" (Dialogue With Trypho, 103). Notice the plural: "apostles" and "those who followed them". The use of the plural matches our four gospels: apostles (Matthew, John) and those who followed them (Mark, Luke). Justin doesn't cite the number four anywhere, but his comments are consistent with the collection of four gospels that sources living just after his time refer to.
Furthermore, if the gospels had initially been anonymous or attributed to other authors, we'd expect that set of circumstances to leave traces in the historical record. Even if the traditional gospel authorship attributions hadn't arisen in our extant sources until Irenaeus, we'd need to explain why the belief is so widespread and apparently so seldom disputed at the time (Irenaeus in France, Clement in Egypt, Hippolytus in Italy, etc.). Even if the pre-Irenaean sources I've cited above didn't exist, the best explanation for the widespread and undisputed nature of the authorship attributions around the time of Irenaeus would be that the attributions originated much earlier and had a lot of credibility. We can cite dozens of non-Christian and Christian sources supporting the traditional authorship attributions in the earliest centuries, and those sources are widespread in their locations, personalities, theologies, and other characteristics. By contrast, the lack of sources Ehrman can cite to support anonymous gospels or early attributions to different authors is pathetic.