I believe that the grey streak in Ash’s hair is a distraction from the true meaning of her name. Everyone else in the movie has a name associated with battle or that implies violence in one way or another. Most are obvious some are not.
Murphy -Irish for sea warrior
Gill (or in some subtitles Jill)- Irish for servant, which would explain why she was sent as bait to meet Ash. She was probably new to her fighting group and was earning her right to a battle name.
Ash – a European tree the favorite wood for making bows, arrows,and spears. The Norse word for spear (ask) and ash are almost identical. Vikings were referred to as the Aescling meaning ‘Men of Ash’.
The name also fits well as a reference to her character. Ash wood is very strong, tough and elastic, and it is written that ash will bear more weight than any other wood.
Here is where I think Oshii is getting Sneaky
The ash is also called Yggdrasil it is the tree Odin hung himself on to seek a vision. It is The World Tree , aka the tree of life. ‘Ash tree’s trunk reached up to the heavens, and in the Underworld, below Yggdrasil’s roots, where the realm of the Dead could be found’ Ash is seen as the axis of the Universe. Ash trees also have a strong connection with flowing water, another favorite symbol of Oshiiâ’s
As to the ‘noble warrior’ Ash’s stoic demeanor and limited food intake some clues can be found in Bushido texts see below.
http://www.sacred-texts.com/shi/bsd/index.htm
chapter IV p.31
“What a coward to cry for a trifling pain! What will you do when your arm is cut off in battle? What when you are called upon to commit hara-kiri?” We all know the pathetic fortitude of a famished little boy-prince of Sendai, who in the drama is made to say to his little page, “Seest thou those tiny sparrows in the nest, how their yellow bills are opened wide, and now see! there comes their mother with worms to feed them. How eagerly and happily the little ones eat! but for a samurai, when his stomach is empty, it is a disgrace to feel hungry.”
chapter XI p.104
It was considered unmanly for a samurai to betray his emotions on his face. “He shows no sign of joy or anger,” was a phrase used, in describing a great character. The most natural affections were kept under control.
Another cryptic reference to who or what ash really is can be found on the soundtrack. Grey Lady is a reference to an obscure Arthurian legend. She is “a ghost lady who protected Arthurs 13 treasures, haunts Moel Arthur.†I am not quite sure what to make of this one just yet.