In the wikia it says that she was serene, white is usually seen as serene but since she is a ghost she is instead grey. That is one theory.
She carried herself in a serene manner
The next is that she is a ghost and that could be the reason.
Another is the fact that it has something to do with her character or some fact about her life. Since all ghost have some reason they are named, like the Bloody Baron, Peeves the Poltergeist, and Nearly Headless Nick.
Below is the definition of "Grey Lady" after I googled it:
grey lady- (Grey Ladies) ghosts of women who supposedly died violently
for the sake of love or pined away from loss of love. The name comes
from their frequent appearance as ladies dressed in grey. Variations
include ladies in white such as the one that frequents Spangler's
Spring in Gettysburg,
So see she did indeed die because of a violent cause so that could be the reason.
Here are some quotes from the wikia:
Many Grey Lady ghosts are known in various locations throughout> England and Wales.
Having fallen fatally ill and on her deathbed, Rowena desperately
asked the Bloody Baron, who was deeply in love with Helena, to find
her daughter and bring her back to her so that she could see her one
last time. Helena tried to hide from him, but the Baron managed to
track her down to a forest in Albania. When she heard the Baron
blundering through the forest toward her, she hid the diadem inside a
hollow tree. Helena refused to come with the Baron and rejected his
affections and he stabbed her in a fit of rage. After seeing what he
had done, remorseful of his action, he stabbed himself to death.
This one shows that she suffered a violent death.