In the synoptic tradition, there are two stories of Jesus being anointed: 1) an episode at Bethany in Judea by an unnamed woman(Mark 14:9 and followed by Matthew) and 2) an episode in Galilee by a woman who is a sinner (Luke 7:37-38).
In the Gospel of John there is also an anointing at Bethany (John 12:1-8). Scholars assume that Mark and John are recording the same event, though John combines elements of Mark's story with details from Luke's story. And John identifies the woman who anoints Jesus at Bethany as Mary, the sister of Martha and Lazarus!
Try this as a challenge: Read the stories side by side and compare and contrast their details. Pay close attention to what John does. Has this author revealed the real identity of the unnamed woman in Mark? Is this conflated oral tradition? Or is this a third anointing?
For a detailed look at John's story and the possibility of a historical kernel, see Volume 1 of Raymond Brown's Anchor Bible commentary on the Gospel of John. From a different perspective, one which argues that Mary is the unnamed woman in Mark, see Richard Bauckham's Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony.
What do you think?