Matthew 26

In the last week of the Savior's ministry, we read - 

"Now when Jesus was in Bethany, in the house of Simon the leper,

7 There came unto him a woman having an alabaster box of very precious ointment, and poured it on his head, as he sat at meat."  (Matthew 26:6–7)

After some dispute amongst His disciples, the Savior declares - 

"...she hath wrought a good work upon me."  (Matthew 26:10)

And - 

"Verily I say unto you, Wheresoever this gospel shall be preached in the whole world, there shall also this, that this woman hath done, be told for a memorial of her."  (Matthew 26:13)

I couldn't find the woman's name.  The scripture only mentions a woman.  Talmage suggests it is Mary, sister to Martha.  It just seems to me that this woman understood what was about to happen to the Savior.