Why Are The Gospels Called Matthew, Mark, Luke, and John?

I recently received an important and puzzling question about the names attached to our four Gospels.  All four books were written and circulated anonymously, and only later did Christian leaders maintain that they were Matthew, Mark, Luke, and John.  Why these names?  Here’s the question:

QUESTION:  I understand why the names John and Matthew ended up being part of the tradition concerning authorship for gospels, but why a tradition for Mark and Luke?  Today, they seem like unlikely character...