UPDATE:

There can be some confusion about __builtins__ or __builtin__. The What’s New In Python 3.0 suggests to use builtins

Renamed module __builtin__ to builtins (removing the underscores, adding an ‘s’). The __builtins__ variable found in most global namespaces is unchanged. To modify a builtin, you should use builtins, not __builtins__!

This may be good if you work with a different Python implementation as the docs indicate:

As an implementation detail, most modules have the name __builtins__ made available as part of their globals. The value of __builtins__ is normally either this module or the value of this module’s __dict__ attribute. Since this is an implementation detail, it may not be used by alternate implementations of Python.

You can get all builtin names with:

>>> import builtins
>>> dir(builtins)

This includes everything from builtins. If you strictly only want the function names, just filter for them:

import types

builtin_function_names = [name for name, obj in vars(builtins).items() 
                          if isinstance(obj, types.BuiltinFunctionType)]

Resulting list in Python 3.6:

['__build_class__',
 '__import__',
 'abs',
 'all',
 'any',
 'ascii',
 'bin',
 'callable',
 'chr',
 'compile',
 'delattr',
 'dir',
 'divmod',
 'eval',
 'exec',
 'format',
 'getattr',
 'globals',
 'hasattr',
 'hash',
 'hex',
 'id',
 'isinstance',
 'issubclass',
 'iter',
 'len',
 'locals',
 'max',
 'min',
 'next',
 'oct',
 'ord',
 'pow',
 'print',
 'repr',
 'round',
 'setattr',
 'sorted',
 'sum',
 'vars',
 'open']

If you want the functions objects, just change your code a little bit by selecting the 'obj' from the dictionary:

builtin_functions = [obj for name, obj in vars(builtins).items() 
                     if isinstance(obj, types.BuiltinFunctionType)]

import __builtin__
import inspect

[name for name, function in sorted(vars(__builtin__).items())
 if inspect.isbuiltin(function) or inspect.isfunction(function)]

There's also the list in the documentation.