In Windows I can hit ENTER while any field is active to Save the entry and start a new one. This make it possible to quickly enter contacts without touching the mouse.
I just tried a Bluetooth keyboard with the Android version of the App and it works more like tab (it just changes focus to the next field). I can’t find any key that saves the entry like it would in Windows.
This behavior is probably the same for USB connected keyboards, but that’s less common on Android.
Right after I drafted this comment I realized that SHIFT-ENTER saves the entry and creates a new one.
That should be fine, so I guess my new request is for this to be documented somewhere. Maybe by making this post it will help someone else who didn’t think to try that.