class myClass(object):
    def __init__(self):
        print self.__class__.__name__
myClass()

>>> def get_called_name(depth=0):
...     return sys._getframe(depth + 1).f_code.co_name
...
>>> class Hello:
...     def __init__(self):
...             print get_called_name()
... 
>>> h = Hello()
__init__
>>>

>>> class A(object):
... 	pass
... 
>>> def f(self):
... 	return sys._getframe().f_code.co_name
... 
>>> A.g = f
>>> a = A()
>>> a.g()
'f'

from new import function, instancemethod
from byteplay import Code, LOAD_CONST, STORE_FAST
from types import MethodType

class A(object):
    def __getattribute__(self, name):
        attr = super(A, self).__getattribute__(name)
        if type(attr) is MethodType and not hasattr(attr.im_func, '_patched'):
            c = Code.from_code(attr.func_code)
            c.code[0:0] = [
                (LOAD_CONST, name),
                (STORE_FAST, '_func_name')]
            f = function(c.to_code(), globals(), attr.__name__)
            f._patched = True
            attr = instancemethod(f, self, A)
            setattr(self, name, attr)
        return attr

    def zzz(self):
        print locals().get('_func_name')

def f(self):
    print locals().get('_func_name')

A.g = f
a = A()
a.zzz()
a.zzz()
a.g()