diff --git a/docs/news.rst b/docs/news.rst
index 51bd5a8a..f7b61cba 100644
--- a/docs/news.rst
+++ b/docs/news.rst
@@ -1,6 +1,11 @@
 Release Notes
 =============
 
+**UNRELEASED**
+
+- Fix naming of the ``data_dir`` directory in the presence of local version segment
+  given via ``egg_info.tag_build`` (PR by Anderson Bravalheri)
+
 **0.41.0 (2023-07-22)**
 
 - Added full support of the build tag syntax to ``wheel tags`` (you can now set a build
diff --git a/src/wheel/bdist_wheel.py b/src/wheel/bdist_wheel.py
index 2f93c473..c8ee2adc 100644
--- a/src/wheel/bdist_wheel.py
+++ b/src/wheel/bdist_wheel.py
@@ -232,6 +232,9 @@ def finalize_options(self):
             bdist_base = self.get_finalized_command("bdist").bdist_base
             self.bdist_dir = os.path.join(bdist_base, "wheel")
 
+        egg_info = self.distribution.get_command_obj("egg_info")
+        egg_info.ensure_finalized()  # needed for correct `wheel_dist_name`
+
         self.data_dir = self.wheel_dist_name + ".data"
         self.plat_name_supplied = self.plat_name is not None
 
diff --git a/tests/test_bdist_wheel.py b/tests/test_bdist_wheel.py
index d2024691..b7c04b27 100644
--- a/tests/test_bdist_wheel.py
+++ b/tests/test_bdist_wheel.py
@@ -6,6 +6,7 @@
 import subprocess
 import sys
 import sysconfig
+from inspect import cleandoc
 from unittest.mock import Mock
 from zipfile import ZipFile
 
@@ -329,3 +330,58 @@ def test_rmtree_readonly(monkeypatch, tmp_path, capsys):
     if expected_count:
         captured = capsys.readouterr()
         assert "file.txt" in captured.stdout
+
+
+def test_data_dir_with_tag_build(monkeypatch, tmp_path):
+    """
+    Setuptools allow authors to set PEP 440's local version segments
+    using ``egg_info.tag_build``. This should be reflected not only in the
+    ``.whl`` file name, but also in the ``.dist-info`` and ``.data`` dirs.
+    See pypa/setuptools#3997.
+    """
+    monkeypatch.chdir(tmp_path)
+    files = {
+        "setup.py": """
+            from setuptools import setup
+            setup(headers=["hello.h"])
+            """,
+        "setup.cfg": """
+            [metadata]
+            name = test
+            version = 1.0
+
+            [options.data_files]
+            hello/world = file.txt
+
+            [egg_info]
+            tag_build = +what
+            tag_date = 0
+            """,
+        "file.txt": "",
+        "hello.h": "",
+    }
+    for file, content in files.items():
+        with open(file, "w", encoding="utf-8") as fh:
+            fh.write(cleandoc(content))
+
+    subprocess.check_call([sys.executable, "setup.py", "bdist_wheel"])
+
+    # Ensure .whl, .dist-info and .data contain the local segment
+    wheel_path = "dist/test-1.0+what-py3-none-any.whl"
+    assert os.path.exists(wheel_path)
+    entries = set(ZipFile(wheel_path).namelist())
+    for expected in (
+        "test-1.0+what.data/headers/hello.h",
+        "test-1.0+what.data/data/hello/world/file.txt",
+        "test-1.0+what.dist-info/METADATA",
+        "test-1.0+what.dist-info/WHEEL",
+    ):
+        assert expected in entries
+
+    for not_expected in (
+        "test.data/headers/hello.h",
+        "test-1.0.data/data/hello/world/file.txt",
+        "test.dist-info/METADATA",
+        "test-1.0.dist-info/WHEEL",
+    ):
+        assert not_expected not in entries