There are no standardized conventions (such as PEPs) for those names. If you check the python stdlib you’ll find lots of different names for those functions.
However, decorator is a rather common name for the decorator function inner.
It is also common to call your wrapped function wrapper and decorate it with functools.wraps(f) with f being the wrapped function (func is also a common name for it).
def decorator_name(whatevs):
def decorator(f):
@wraps(f)
def wrapper(*args, **kwargs):
pass # sweet decorator goodness
return wrapper
return decorator