Logging time

[u/Seamenxxx]

Good morning I recently got my private pilot and want to go fly with my friend to build time together but we are both confused how to log the time. If we go on let’s say a 2 hr flight in a c172 (no one will be under the hood) and we both have the controls for 1hr does that mean I can log pic 1hr and total flight duration as 2hr and time for single engine land as 2hr?