In this context "common" refers to the node that is common to both the input and output -- i.e., the common node is either the ground or power supply node that is shared between input and output (and is a small signal ground).
Here is a simple common collector circuit:
Source: Wikimedia
Notice that the transistor's collector (marked "C") is connected to the power supply (which is also small signal ground) and the output is taken from the emitter.
Here is a simple common emitter circuit:
Source: Wikimedia
In this case the emitter is connected to ground, and the output is taken from the collector.
More realistic circuits will often have additional resistors, such as this common emitter with an emitter degeneration resistor:
Source: Wikimedia
This is trickier since neither the collector nor the emitter are connected directly to either ground or the power supply. Nonetheless, the emitter node is "common" to both the input and output. Like the basic common emitter, the output is still taken at the collector -- so this too is a common emitter circuit.
The circuit you've shown has its output at the emitter and the collector is connected to the power supply just like the simple common collector circuit I've shown above.