Complementary transistor pair with a bipolar transistor and a MOSFET
This is what's called a gate drive circuit, or gate driver. The BC558 aids in pulling charge out of the IRF840's gate, acting as a current amplifier to turn the FET off faster. The circuit designer apparently decided that the turn-on time wasn't as much of a concern, so a 1N4148 diode is used to pass the un-amplified current straight from the PIC's output.

The term gate driver is a generic term, referring to any circuit that aids a signal in charging and/or discharging the gate of a FET or IGBT. I don't think the particular instance in the circuit above has any more specific name.