diff --git a/modin/experimental/core/execution/native/implementations/hdk_on_native/calcite_builder.py b/modin/experimental/core/execution/native/implementations/hdk_on_native/calcite_builder.py
index edeac113655..bd56ac7bab0 100644
--- a/modin/experimental/core/execution/native/implementations/hdk_on_native/calcite_builder.py
+++ b/modin/experimental/core/execution/native/implementations/hdk_on_native/calcite_builder.py
@@ -738,6 +738,18 @@ def _push(self, node):
         node : CalciteBaseNode
             A node to add.
         """
+        if (
+            len(self.res) != 0
+            and isinstance(node, CalciteProjectionNode)
+            and isinstance(self.res[-1], CalciteProjectionNode)
+            and all(isinstance(expr, CalciteInputRefExpr) for expr in node.exprs)
+        ):
+            # Replace the last CalciteProjectionNode with this one and
+            # translate the input refs.
+            exprs = self.res.pop().exprs
+            node = CalciteProjectionNode(
+                node.fields, [exprs[expr.input] for expr in node.exprs]
+            )
         self.res.append(node)
 
     def _last(self):
diff --git a/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/dataframe.py b/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/dataframe.py
index 317eeb45549..89cd0bc5468 100644
--- a/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/dataframe.py
+++ b/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/dataframe.py
@@ -2041,9 +2041,7 @@ def _materialize(self):
                 new_table, unsupported_cols=[], encode_col_names=False
             )[0]
         else:
-            partitions = self._partition_mgr_cls.run_exec_plan(
-                self._op, self._table_cols
-            )
+            partitions = self._partition_mgr_cls.run_exec_plan(self._op)
 
         self._partitions = partitions
         self._op = FrameNode(self)
diff --git a/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/utils.py b/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/utils.py
index 14d48f379ce..5fb2d01dfe8 100644
--- a/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/utils.py
+++ b/modin/experimental/core/execution/native/implementations/hdk_on_native/dataframe/utils.py
@@ -429,12 +429,12 @@ def to_empty_pandas_df(df):
         index_cols = None
     else:
         index_cols = ColNameCodec.mangle_index_names(merged.index.names)
-        for orig_name, mangled_name in zip(merged.index.names, index_cols):
+        for name in index_cols:
             # Using _dtypes here since it contains all column names,
             # including the index.
-            df = left if mangled_name in left._dtypes else right
-            exprs[orig_name] = df.ref(mangled_name)
-            new_dtypes.append(df._dtypes[mangled_name])
+            df = left if name in left._dtypes else right
+            exprs[name] = df.ref(name)
+            new_dtypes.append(df._dtypes[name])
 
     left_col_names = set(left.columns)
     right_col_names = set(right.columns)
diff --git a/modin/experimental/core/execution/native/implementations/hdk_on_native/partitioning/partition_manager.py b/modin/experimental/core/execution/native/implementations/hdk_on_native/partitioning/partition_manager.py
index b90a9161b32..dd242bee9d3 100644
--- a/modin/experimental/core/execution/native/implementations/hdk_on_native/partitioning/partition_manager.py
+++ b/modin/experimental/core/execution/native/implementations/hdk_on_native/partitioning/partition_manager.py
@@ -227,7 +227,7 @@ def is_supported_dtype(dtype):
         )
 
     @classmethod
-    def run_exec_plan(cls, plan, columns):
+    def run_exec_plan(cls, plan):
         """
         Run execution plan in HDK storage format to materialize frame.
 
@@ -235,8 +235,6 @@ def run_exec_plan(cls, plan, columns):
         ----------
         plan : DFAlgNode
             A root of an execution plan tree.
-        columns : list of str
-            A frame column names.
 
         Returns
         -------
@@ -256,10 +254,6 @@ def run_exec_plan(cls, plan, columns):
             calcite_json = "execute calcite " + calcite_json
         table = worker.executeRA(calcite_json)
 
-        # workaround for https://github.com/modin-project/modin/issues/1851
-        if DoUseCalcite.get():
-            table._column_names = [ColNameCodec.encode(c) for c in columns]
-
         res = np.empty((1, 1), dtype=np.dtype(object))
         res[0][0] = cls._partition_class(table)