Tertullian, in his Apologeticum bears witness to the fact that even by the third century, little was known about the Christians. Interestingly enough, several people, including Tertullian, attest to the fact that Christians were constantly called the wrong name – ‘Chrestianus’, as Tertullian says:
Sed et cum perperam “Chrestianus” pronuntiatur a vobis… (Apologeticum, 3.5)
“And even when it is said wrongly ‘Chrestian’ by you…”
It’s interesting that Suetonius notes, in his life of Claudius, that the ‘Jews’ were expelled at the ‘instigation of Chrestus’ (Iudaeos impulsore Chresto assidue tumultuantis). However, in his life of Nero, he gets the name right (Christiani), which I find odd. I wonder if there’s any textual variation in that part.