DeltaT - Time is logged as copilot. When the SO runs the leg he/she will do so in the same manner as when the Captain or the FO runs their leg. There is very little planning to do.
You can call the SO role whatever you like. You're not looked down on or treated differently. The only difference is that after setting up the flight deck on your leg you jump out of the seat prior to pushback and then jump back in at 20k.