J = L + S , L + S – 1, … , |L – S|

J = 0 corresponds to parallel but pointing in opposite directions.

J = 1 corresponds to perpendicular.

J = 2 corresponds to parallel and pointing in the same direction.

My reasoning for this: L and S are both spin 1, their projection to the z-axis m_L or m_S = 1, 0, -1.

When m_L = m_S = +-1 (so L and S parallel pointing in the same direction), this corresponds to m_J = m_S + m_L = +-2, which corresponds to J = 2.

When m_L = -m_S = +-1 (so L and S parallel pointing in the opposite direction), this corresponds to m_J = 0, which corresponds to J = 0.

When m_L or m_S = 0 with the other being +-0 (so L or S being “perpendicular”, while the other one is parallel pointing up or down), this corresponds to m_J = +-1, which corresponds to J = 1.