Change PyPI project name to simply `mypy` (#2682)

diff --git a/README.md b/README.md
index 1653f1e..d4db725 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@
 =======================================
 
 [![Build Status](https://travis-ci.org/python/mypy.svg)](https://travis-ci.org/python/mypy)
-[![Chat at https://gitter.im/python/mypy](https://badges.gitter.im/python/mypy.svg)](https://gitter.im/python/mypy?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge) 
+[![Chat at https://gitter.im/python/mypy](https://badges.gitter.im/python/mypy.svg)](https://gitter.im/python/mypy?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
 
 
 Got a question? File an issue!
@@ -75,9 +75,7 @@
 
 Mypy can be installed using pip:
 
-    $ python3 -m pip install -U mypy-lang
-
-*Note that the package name is `mypy-lang`, not `mypy`.*
+    $ python3 -m pip install -U mypy
 
 If you want to run the latest version of the code, you can install from git:
 
@@ -113,9 +111,7 @@
 Depending on your configuration, you may have to run `pip3` like
 this:
 
-    $ python3 -m pip install -U mypy-lang
-
-Double-check that you installed `mypy-lang`, not `mypy`.
+    $ python3 -m pip install -U mypy
 
 Except on Windows, it's best to always use the `--fast-parser`
 option to mypy; this requires installing `typed-ast`:
diff --git a/docs/source/common_issues.rst b/docs/source/common_issues.rst
index 9aaefb5..3477d90 100644
--- a/docs/source/common_issues.rst
+++ b/docs/source/common_issues.rst
@@ -14,10 +14,9 @@
 
 If installation fails, you've probably hit one of these issues:
 
-* The package name is **mypy-lang** -- *not* just mypy.
 * Mypy needs Python 3.3 or later to run.
 * You may have to run pip like this:
-  ``python3 -m pip install mypy-lang``.
+  ``python3 -m pip install mypy``.
 
 .. _annotations_needed:
 
diff --git a/docs/source/getting_started.rst b/docs/source/getting_started.rst
index 98f4d30..a41c125 100644
--- a/docs/source/getting_started.rst
+++ b/docs/source/getting_started.rst
@@ -10,9 +10,7 @@
 
 .. code-block:: text
 
-    $ python3 -m pip install mypy-lang
-
-Note that the package name is ``mypy-lang`` and not just ``mypy``, as unfortunately the ``mypy`` PyPI name is not available.
+    $ python3 -m pip install mypy
 
 Installing from source
 **********************
diff --git a/setup.py b/setup.py
index 722fab8..ec62117 100644
--- a/setup.py
+++ b/setup.py
@@ -104,7 +104,7 @@
 if sys.version_info < (3, 5):
     install_requires.append('typing >= 3.5.3')
 
-setup(name='mypy-lang',
+setup(name='mypy',
       version=version,
       description=description,
       long_description=long_description,