What is name of this oscillator and how does it work?
It’s a common base Colpitts oscillator. Positive (oscillatory) feedback from collector to emitter (the emitter is used as an input). With C1 and C2 the same value, the frequency is dictated by the collector inductance and half of C1. It works more effectively with a decoupling capacitor across R3. If you take a look at my profile and some of the answers I’ve previously given, you’ll find much more detailed explanations of generally, how this type of oscillator works.