diff --git a/python35.rpmlintrc b/python3.5.rpmlintrc
similarity index 100%
rename from python35.rpmlintrc
rename to python3.5.rpmlintrc
diff --git a/python35.spec b/python3.5.spec
similarity index 99%
rename from python35.spec
rename to python3.5.spec
index 90b206a..bd57875 100644
--- a/python35.spec
+++ b/python3.5.spec
@@ -79,7 +79,7 @@
 # ==================
 # Top-level metadata
 # ==================
-Name: python%{pyshortver}
+Name: python%{pybasever}
 Summary: Version %{pybasever} of the Python programming language
 URL: https://www.python.org/
 
@@ -87,7 +87,7 @@ URL: https://www.python.org/
 #global prerel ...
 %global upstream_version %{general_version}%{?prerel}
 Version: %{general_version}%{?prerel:~%{prerel}}
-Release: 4%{?dist}
+Release: 5%{?dist}
 License: Python
 
 # Whether to use RPM build wheels from the python-{pip,setuptools}-wheel package
@@ -160,8 +160,9 @@ Requires: glibc%{?_isa} >= 2.24.90-26
 
 BuildRequires: python-rpm-macros
 
-# People might want to dnf install pythonX.Y instead of pythonXY
-Provides: python%{pybasever} = %{version}-%{release}
+# Provide and obsolete the old python3X name
+Provides:  python%{pyshortver} = %{version}-%{release}
+Obsoletes: python%{pyshortver} < %{version}-%{release}
 
 # =======================
 # Source code and patches
@@ -1068,6 +1069,9 @@ CheckPython optimized
 # ======================================================
 
 %changelog
+* Wed May 06 2020 Miro Hrončok <mhroncok@redhat.com> - 3.5.9-5
+- Rename from python35 to python3.5
+
 * Tue May 05 2020 Tomas Hrnciar <thrnciar@redhat.com> - 3.5.9-4
 - Fix a build/test failure with glibc 2.31.9000+ (#1819759)
 
diff --git a/tests/tests.yml b/tests/tests.yml
index fa2e2de..9b1b30e 100644
--- a/tests/tests.yml
+++ b/tests/tests.yml
@@ -14,4 +14,4 @@
     required_packages:
     - gcc
     - python3-tox
-    - python35
+    - python3.5