In EDH/Commander, what is the 'color identity' of a double-faced card?
Yes, both sides of DFC count towards its color identity.

903.4c The back face of a double-faced card (see rule 711) is included when determining a card's color identity.
Example: Civilized Scholar is the front face of a double-faced card with mana cost
{2}{U}. Homicidal Brute is the back face of that double-faced card and has a red color
indicator. The card's color identity is blue and red.

So, Elbrus can only be used in a Commander deck where Black is part of your Commander's color identity.