I believe Nadi shodhana is the name normally given to alternate nostril breathing when you breathe out and in once only through one nostril and then change to the other. This is also called anulom vilom or sukha pranayama. When you breathe in and out several times only through the left nostril this is called sri chandra pranayama, and breathing in and out through the right nostril only is called sri surya pranayama. So what you are describing is a combined form of these latter two. They are normally practiced in succession in order to balance the subtle body.
Is there a name for breathing in through both sides & out through the left, then next time out through the right but always breathing in through both sides?