diff --git a/backend/src/hatchling/metadata/core.py b/backend/src/hatchling/metadata/core.py
index 743dd0fd5..23bba1905 100644
--- a/backend/src/hatchling/metadata/core.py
+++ b/backend/src/hatchling/metadata/core.py
@@ -962,7 +962,7 @@ def classifiers(self) -> list[str]:
                 message = 'Field `project.classifiers` must be an array'
                 raise TypeError(message)
 
-            verify_classifiers = not os.environ.get("HATCH_NO_VERIFY_TROVE_CLASSIFIERS")
+            verify_classifiers = not os.environ.get('HATCH_METADATA_CLASSIFIERS_NO_VERIFY')
             if verify_classifiers:
                 import trove_classifiers
 
@@ -979,7 +979,11 @@ def classifiers(self) -> list[str]:
                     message = f'Classifier #{i} of field `project.classifiers` must be a string'
                     raise TypeError(message)
 
-                if not self.__classifier_is_private(classifier) and verify_classifiers and classifier not in known_classifiers:
+                if (
+                    not self.__classifier_is_private(classifier)
+                    and verify_classifiers
+                    and classifier not in known_classifiers
+                ):
                     message = f'Unknown classifier in field `project.classifiers`: {classifier}'
                     raise ValueError(message)
 
diff --git a/tests/backend/metadata/test_core.py b/tests/backend/metadata/test_core.py
index 3673d770c..2795c694d 100644
--- a/tests/backend/metadata/test_core.py
+++ b/tests/backend/metadata/test_core.py
@@ -899,14 +899,14 @@ def test_entry_not_string(self, isolation):
             _ = metadata.core.classifiers
 
     def test_entry_unknown(self, isolation, monkeypatch):
-        monkeypatch.delenv("HATCH_NO_VERIFY_TROVE_CLASSIFIERS", False)
+        monkeypatch.delenv('HATCH_METADATA_CLASSIFIERS_NO_VERIFY', False)
         metadata = ProjectMetadata(str(isolation), None, {'project': {'classifiers': ['foo']}})
 
         with pytest.raises(ValueError, match='Unknown classifier in field `project.classifiers`: foo'):
             _ = metadata.core.classifiers
 
     def test_entry_unknown_no_verify(self, isolation, monkeypatch):
-        monkeypatch.setenv("HATCH_NO_VERIFY_TROVE_CLASSIFIERS", "1")
+        monkeypatch.setenv('HATCH_METADATA_CLASSIFIERS_NO_VERIFY', '1')
         classifiers = [
             'Programming Language :: Python :: 3.11',
             'Programming Language :: Python :: 3.11',