Yes, your intuition is correct.
Your model is something like this:
(utility) = X1 * (Price estimate) + X2 * (Brand A estimate) + X1*X2*(Brand A x Price Interaction estimate) + ...
So in this case, X2 should be 0 or 1 (Is it Brand A or not?), and X1 should be price (zero-centered it sounds like). That equation should continue on for each Brand and Brand/Price interaction. So for each interaction, there should be a 0 or 1 (is it this Brand or isn't it), a price level, and the estimate of the interaction effect, all multiplied together.