Why are there differences in events within the Gospels? Why does the gospel of Matthew claim that it was Mary Magdalene who annointed Jesus's feet with oil and Luke claim it was an unnamed woman?
In the Luke account of Jesus being anointed, a woman is recorded as being 'a sinner' and she is unnamed. In the Matthew account of Jesus being anointed, a woman is identified as Mary, the sister of Martha and Lazarus.

Examination of these two accounts shows that it is impossible to prove that they are the same incident. The details are so worded that one cannot say, categorically, that these are not two accounts of different events.

Thus the unnamed 'sinner' cannot be identified. Whoever she is or is not, it cannot be proven.

All we know of this unidentified woman is that she anointed Jesus prior to his sufferings, death and burial.

In so doing, she was successful, anointing Jesus beforehand, for the women who went to the tomb with spices, after his decease, were not able to administer them, for Jesus was risen from the dead by the time they got there.

The four gospels are clearly demonstrating different aspects of Jesus Christ and his ministry on earth. The details supplied in the four aspect-accounts are selected with an overall purpose in mind. Different events, sometimes not in consecutive order of occurrence, are gathered together and presented in juxtaposition in order to convey a particular aspect of the Person and Ministry of Jesus Christ, the Son of God.