diff --git a/distributed/protocol/pickle.py b/distributed/protocol/pickle.py
index 90f0fa3f88f..8b4b7328e5b 100644
--- a/distributed/protocol/pickle.py
+++ b/distributed/protocol/pickle.py
@@ -10,7 +10,7 @@
 
 from distributed.protocol.serialize import dask_deserialize, dask_serialize
 
-CLOUDPICKLE_GTE_20 = parse_version(cloudpickle.__version__) >= parse_version("2.0.0")
+CLOUDPICKLE_GE_20 = parse_version(cloudpickle.__version__) >= parse_version("2.0.0")
 
 HIGHEST_PROTOCOL = pickle.HIGHEST_PROTOCOL
 
@@ -68,7 +68,7 @@ def dumps(x, *, buffer_callback=None, protocol=HIGHEST_PROTOCOL):
             pickler.dump(x)
             result = f.getvalue()
         if b"__main__" in result or (
-            CLOUDPICKLE_GTE_20
+            CLOUDPICKLE_GE_20
             and getattr(inspect.getmodule(x), "__name__", None)
             in cloudpickle.list_registry_pickle_by_value()
         ):
diff --git a/distributed/protocol/tests/test_pickle.py b/distributed/protocol/tests/test_pickle.py
index 52b5649cae3..611c95a07fb 100644
--- a/distributed/protocol/tests/test_pickle.py
+++ b/distributed/protocol/tests/test_pickle.py
@@ -14,7 +14,7 @@
 from distributed import profile
 from distributed.protocol import deserialize, serialize
 from distributed.protocol.pickle import (
-    CLOUDPICKLE_GTE_20,
+    CLOUDPICKLE_GE_20,
     HIGHEST_PROTOCOL,
     dumps,
     loads,
@@ -201,7 +201,7 @@ def funcs():
 
 
 @pytest.mark.skipif(
-    not CLOUDPICKLE_GTE_20, reason="Pickle by value registration not supported"
+    not CLOUDPICKLE_GE_20, reason="Pickle by value registration not supported"
 )
 def test_pickle_by_value_when_registered():
     with save_sys_modules():
diff --git a/distributed/shuffle/tests/test_merge.py b/distributed/shuffle/tests/test_merge.py
index 4ea17c6df1d..99e4c32d65c 100644
--- a/distributed/shuffle/tests/test_merge.py
+++ b/distributed/shuffle/tests/test_merge.py
@@ -9,7 +9,7 @@
 dd = pytest.importorskip("dask.dataframe")
 import pandas as pd
 
-from dask.dataframe._compat import PANDAS_GT_200, tm
+from dask.dataframe._compat import PANDAS_GE_200, tm
 from dask.dataframe.utils import assert_eq
 from dask.utils_test import hlg_layer_topological
 
@@ -249,7 +249,7 @@ async def test_merge_by_multiple_columns(c, s, a, b, how):
                 # FIXME: There's an discrepancy with an empty index for
                 # pandas=2.0 (xref https://github.com/dask/dask/issues/9957).
                 # Temporarily avoid index check until the discrepancy is fixed.
-                check_index=not (PANDAS_GT_200 and expected.index.empty),
+                check_index=not (PANDAS_GE_200 and expected.index.empty),
             )
 
             expected = pdr.join(pdl, how=how)
@@ -259,7 +259,7 @@ async def test_merge_by_multiple_columns(c, s, a, b, how):
                 # FIXME: There's an discrepancy with an empty index for
                 # pandas=2.0 (xref https://github.com/dask/dask/issues/9957).
                 # Temporarily avoid index check until the discrepancy is fixed.
-                check_index=not (PANDAS_GT_200 and expected.index.empty),
+                check_index=not (PANDAS_GE_200 and expected.index.empty),
             )
 
             expected = pd.merge(pdl, pdr, how=how, left_index=True, right_index=True)
@@ -278,7 +278,7 @@ async def test_merge_by_multiple_columns(c, s, a, b, how):
                 # FIXME: There's an discrepancy with an empty index for
                 # pandas=2.0 (xref https://github.com/dask/dask/issues/9957).
                 # Temporarily avoid index check until the discrepancy is fixed.
-                check_index=not (PANDAS_GT_200 and expected.index.empty),
+                check_index=not (PANDAS_GE_200 and expected.index.empty),
             )
 
             expected = pd.merge(pdr, pdl, how=how, left_index=True, right_index=True)
@@ -297,7 +297,7 @@ async def test_merge_by_multiple_columns(c, s, a, b, how):
                 # FIXME: There's an discrepancy with an empty index for
                 # pandas=2.0 (xref https://github.com/dask/dask/issues/9957).
                 # Temporarily avoid index check until the discrepancy is fixed.
-                check_index=not (PANDAS_GT_200 and expected.index.empty),
+                check_index=not (PANDAS_GE_200 and expected.index.empty),
             )
 
             # hash join