That said...

What's the benefit of it being a decorator?  The docstring?  Access to func.__name__?  It could just as well be:

    class attribute:
        _name = None
        def __get__(self, instance, owner):
            if instance is None:
                return self
            if self._name is None:
                for name, attr in vars(owner).items():
                    if attr is self:
                        self._name = name
                        break
            return instance.__dict__[self._name]

However, note that this is a non-data descriptor since it lacks __set__ and __delete__.  That means it is *not* a read-only wrapper like property.  If that's not a concern then there's no point to using a descriptor at all since you can just use a constant as a place-holder:

    class Bar:
        x = ...
        def __init__(self):
            self.x = 42

If you *are* looking for a read-only wrapping descriptor then you'll need __set__ and __delete__ methods, likely ones that simply raise AttributeError.

FWIW, there are definitely plenty of useful things you can do with descriptors. [1]  Some could be useful enough to make it into the stdlib (or builtins), but I'm not convinced the one you are proposing has enough justification at this point.

[1] https://bitbucket.org/ericsnowcurrently/presentations/src/default/utpy-may2015/