Print as array from the console:
print([k.name for k in C.active_object.data.shape_keys.key_blocks])

Print as list from the console:
for k in C.active_object.data.shape_keys.key_blocks:
    print(k.name)

Prefix either with these two lines if you want to run it as a script from the text editor:
import bpy
C = bpy.context