diff --git a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
index b6c89d484c..c87817e0fa 100644
--- a/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
+++ b/sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/optimizer/Optimizer.scala
@@ -516,10 +516,34 @@ object RemoveRedundantAliases extends Rule[LogicalPlan] {
  * Remove no-op operators from the query plan that do not make any modifications.
  */
 object RemoveNoopOperators extends Rule[LogicalPlan] {
+  def restoreOriginalOutputNames(
+      projectList: Seq[NamedExpression],
+      originalNames: Seq[String]): Seq[NamedExpression] = {
+    projectList.zip(originalNames).map {
+      case (attr: Attribute, name) => attr.withName(name)
+      case (alias: Alias, name) => alias.withName(name)
+      case (other, _) => other
+    }
+  }
+
   def apply(plan: LogicalPlan): LogicalPlan = plan.transformUpWithPruning(
     _.containsAnyPattern(PROJECT, WINDOW), ruleId) {
     // Eliminate no-op Projects
-    case p @ Project(_, child) if child.sameOutput(p) => child
+    case p @ Project(projectList, child) if child.sameOutput(p) =>
+      val newChild = child match {
+        case p: Project =>
+          p.copy(projectList = restoreOriginalOutputNames(p.projectList, projectList.map(_.name)))
+        case agg: Aggregate =>
+          agg.copy(aggregateExpressions =
+            restoreOriginalOutputNames(agg.aggregateExpressions, projectList.map(_.name)))
+        case _ =>
+          child
+      }
+      if (newChild.output.zip(projectList).forall { case (a1, a2) => a1.name == a2.name }) {
+        newChild
+      } else {
+        p
+      }
 
     // Eliminate no-op Window
     case w: Window if w.windowExpressions.isEmpty => w.child
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/RemoveNoopOperatorsSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/RemoveNoopOperatorsSuite.scala
index cedd21d2bf..943d207ddc 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/RemoveNoopOperatorsSuite.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/optimizer/RemoveNoopOperatorsSuite.scala
@@ -54,4 +54,16 @@ class RemoveNoopOperatorsSuite extends PlanTest {
 
     comparePlans(optimized, testRelation)
   }
+
+  test("SPARK-36353: RemoveNoopOperators should keep output schema") {
+    val query = testRelation
+      .select(('a + 'b).as("c"))
+      .analyze
+    val originalQuery = Project(Seq(query.output.head.withName("C")), query)
+    val optimized = Optimize.execute(originalQuery.analyze)
+    val result = testRelation
+      .select(('a + 'b).as("C"))
+      .analyze
+    comparePlans(optimized, result)
+  }
 }