Here's a thread in which James McGrath, a liberal New Testament scholar, and some commenters question the widespread claim that the gospels originally circulated as anonymous documents. There are many reasons to reject the notion that the gospels were initially anonymous. Anybody who's interested can search this blog's archives for my posts on the subject. When people like McGrath and his commenters are so critical of the anonymity of the gospels, that's significant.
The issue of why Matthew would use Mark's material repeatedly comes up in McGrath's thread. I've written on the subject elsewhere, like here. The theory that the fourth gospel was written by some John other than the apostle also comes up. I've addressed that argument many times, such as here.