I think the previous guy was using a wired door sensor.
Assuming you are using a wireless door sensor on the entry/exit door and it is setup as a group 10...here's the logic:
1. By default, if there is no exit after arrming the motion button, the system will turn the motion off, this is to prevent false alarms because most people do not use a motion while at home, they will trigger it by moving around, However, I know some setups can use this if the motion is in another area of the house, etc.
2. You can make your motion active with the Doors button by programming it as a 15. There is no delay though.
Changing the name does nothing, its just there for us humans.
If you arm both then leave, or at least open and close the door (e/e sensor) - or use the keyfob to arm the motion will stay on. (group 17).
Please explain further if this doesnt help.