Question: Scenario: power outlet in the yard for electric vehicle, to avoid running an ugly extension from inside home and leaving an open window; I need to avoid that anyone just comes and uses my power though.

Enter the switch I'm looking for.

This would be the operational flow:

1. Attach the charging cable of the vehicle to the outdoor outlet (no current will flow since the outlet is not powered - yet)
2. get inside, arm said switch, current will start flowing as the vehicle begins charging, and the switch will stay on
3. Either the vehicle stops charging, or I unplug it, or someone else does because they want to use my energy for free: the switch will detect no more current flowing through it, and will disarm, leaving the outdoor outlet inactive

I found two somewhat similar questions:

[Need a switch/circuit breaker that stops power supply to equipment when power comes back after outage](https://electronics.stackexchange.com/questions/384591/need-a-switch-circuit-breaker-that-stops-power-supply-to-equipment-when-power-co) (not good for me, since it is intended to check for incoming power, not outgoing current flow)

[I'm looking for a circuit breaker that interrupts the circuit when current drops to zero](https://electronics.stackexchange.com/questions/487375/im-looking-for-a-circuit-breaker-that-interrupts-the-circuit-when-current-drops) (not good, as it is for DC rather than AC)

Is there a name for this peculiar kind of switch, and/or is DIY easily accessible?

Answer: 
There are control panels for pool/submersible pumps with dry run protection (switch off when current is below a setup value). Maybe you find some one-phase starter that can fit your needs.
If a fixed power-on time is acceptable, then a lamp timer or bathroom heat lamp/fan timer can be wired in series with the outlet. This would make power available for 4 hours (for example) no matter how dead the vehicle's batteries are. Granted, someone could still come up and steal your power, but not for very long, and not at all after the timed period (like overnight). If nothing else, this is a temporary solution until you get a sensing circuit built.