diff --git a/news/6056.bugfix.rst b/news/6056.bugfix.rst
new file mode 100644
index 00000000..8ff134e3
--- /dev/null
+++ b/news/6056.bugfix.rst
@@ -0,0 +1 @@
+Fix a bug with locking projects that contains packages with non canonical names from private indexes
diff --git a/pipenv/patched/pip/_internal/resolution/resolvelib/factory.py b/pipenv/patched/pip/_internal/resolution/resolvelib/factory.py
index fb8274a5..250006ad 100644
--- a/pipenv/patched/pip/_internal/resolution/resolvelib/factory.py
+++ b/pipenv/patched/pip/_internal/resolution/resolvelib/factory.py
@@ -247,6 +247,7 @@ class Factory:
         # Hopefully the Project model can correct this mismatch in the future.
         template = ireqs[0]
         assert template.req, "Candidates found on index must be PEP 508"
+        project_name = template.req.name
         name = canonicalize_name(template.req.name)
 
         extras: FrozenSet[str] = frozenset()
@@ -282,7 +283,7 @@ class Factory:
 
         def iter_index_candidate_infos() -> Iterator[IndexCandidateInfo]:
             result = self._finder.find_best_candidate(
-                project_name=name,
+                project_name=project_name,
                 specifier=specifier,
                 hashes=hashes,
             )
diff --git a/tests/integration/test_lock.py b/tests/integration/test_lock.py
index 0259f6ba..99f5cd55 100644
--- a/tests/integration/test_lock.py
+++ b/tests/integration/test_lock.py
@@ -285,6 +285,33 @@ pipenv-test-private-package = {version = "*", index = "testpypi"}
         assert c.returncode == 0
 
 
+@pytest.mark.lock
+@pytest.mark.index
+@pytest.mark.install  # private indexes need to be uncached for resolution
+@pytest.mark.requirements
+@pytest.mark.needs_internet
+def test_private_index_lock_requirements_for_not_canonical_package(pipenv_instance_private_pypi):
+    with pipenv_instance_private_pypi() as p:
+        with open(p.pipfile_path, 'w') as f:
+            contents = """
+[[source]]
+url = "https://pypi.org/simple"
+verify_ssl = true
+name = "pypi"
+
+[[source]]
+url = "https://test.pypi.org/simple"
+verify_ssl = true
+name = "testpypi"
+
+[packages]
+pipenv_test_private_package = {version = "*", index = "testpypi"}
+            """.strip()
+            f.write(contents)
+        c = p.pipenv('lock')
+        assert c.returncode == 0
+
+
 @pytest.mark.index
 @pytest.mark.install
 def test_lock_updated_source(pipenv_instance_private_pypi):