Yes, I do think the association of the color gray with depression is apt, but I do think that there are more layers to it as well. I interpreted the game as one about loss (in particular death)*- rather than seeing the crumbling statues as a representation of her own ego, I thought of them as symbolizing a lost loved one- perhaps a maternal figure, friend/mentor, or even a lover. In that context, I think the symbolism of the name could be that of the ambiguity of grayness, a kind of "in-betweenness"- a transitional point between the bright white (innocence- or perhaps numbness?) of the intro to the blackness (grief) that chases Gris throughout the story, which she must eventually confront.

*[SPOILER] Interestingly, I got an achievement at the end of the game called "Acceptance", and looking it up there are more such achievements named after the 5 stages of grief. The achievements for completing the level do support the interpretation of Gris as "being without color"as well, as completing each stage "brought a color back".