diff --git a/cpp/velox/operators/functions/RegistrationAllFunctions.cc b/cpp/velox/operators/functions/RegistrationAllFunctions.cc
index 638dbcccff0c..6b6564fa4aa3 100644
--- a/cpp/velox/operators/functions/RegistrationAllFunctions.cc
+++ b/cpp/velox/operators/functions/RegistrationAllFunctions.cc
@@ -52,9 +52,6 @@ void registerFunctionOverwrite() {
   velox::registerFunction<RoundFunction, int64_t, int64_t, int32_t>({"round"});
   velox::registerFunction<RoundFunction, double, double, int32_t>({"round"});
   velox::registerFunction<RoundFunction, float, float, int32_t>({"round"});
-  // TODO: the below rand function registry can be removed after presto function registry is removed.
-  velox::registerFunction<velox::functions::sparksql::RandFunction, double, velox::Constant<int32_t>>({"spark_rand"});
-  velox::registerFunction<velox::functions::sparksql::RandFunction, double, velox::Constant<int64_t>>({"spark_rand"});
 
   auto kRowConstructorWithNull = RowConstructorWithNullCallToSpecialForm::kRowConstructorWithNull;
   velox::exec::registerVectorFunction(
@@ -74,10 +71,6 @@ void registerFunctionOverwrite() {
   velox::exec::registerFunctionCallToSpecialForm(
       kRowConstructorWithAllNull,
       std::make_unique<RowConstructorWithNullCallToSpecialForm>(kRowConstructorWithAllNull));
-  velox::functions::registerBinaryIntegral<velox::functions::CheckedPlusFunction>({"check_add"});
-  velox::functions::registerBinaryIntegral<velox::functions::CheckedMinusFunction>({"check_subtract"});
-  velox::functions::registerBinaryIntegral<velox::functions::CheckedMultiplyFunction>({"check_multiply"});
-  velox::functions::registerBinaryIntegral<velox::functions::CheckedDivideFunction>({"check_divide"});
 
   velox::functions::registerPrestoVectorFunctions();
 }
diff --git a/gluten-core/src/main/scala/org/apache/gluten/expression/ExpressionConverter.scala b/gluten-core/src/main/scala/org/apache/gluten/expression/ExpressionConverter.scala
index da5625cd45e5..d5222cfc6350 100644
--- a/gluten-core/src/main/scala/org/apache/gluten/expression/ExpressionConverter.scala
+++ b/gluten-core/src/main/scala/org/apache/gluten/expression/ExpressionConverter.scala
@@ -564,7 +564,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           tryEval,
-          ExpressionNames.CHECK_ADD
+          ExpressionNames.CHECKED_ADD
         )
       case tryEval @ TryEval(a: Subtract) =>
         BackendsApiManager.getSparkPlanExecApiInstance.genTryArithmeticTransformer(
@@ -572,7 +572,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           tryEval,
-          ExpressionNames.CHECK_SUBTRACT
+          ExpressionNames.CHECKED_SUBTRACT
         )
       case tryEval @ TryEval(a: Divide) =>
         BackendsApiManager.getSparkPlanExecApiInstance.genTryArithmeticTransformer(
@@ -580,7 +580,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           tryEval,
-          ExpressionNames.CHECK_DIVIDE
+          ExpressionNames.CHECKED_DIVIDE
         )
       case tryEval @ TryEval(a: Multiply) =>
         BackendsApiManager.getSparkPlanExecApiInstance.genTryArithmeticTransformer(
@@ -588,7 +588,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           tryEval,
-          ExpressionNames.CHECK_MULTIPLY
+          ExpressionNames.CHECKED_MULTIPLY
         )
       case a: Add =>
         BackendsApiManager.getSparkPlanExecApiInstance.genArithmeticTransformer(
@@ -596,7 +596,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           a,
-          ExpressionNames.CHECK_ADD
+          ExpressionNames.CHECKED_ADD
         )
       case a: Subtract =>
         BackendsApiManager.getSparkPlanExecApiInstance.genArithmeticTransformer(
@@ -604,7 +604,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           a,
-          ExpressionNames.CHECK_SUBTRACT
+          ExpressionNames.CHECKED_SUBTRACT
         )
       case a: Multiply =>
         BackendsApiManager.getSparkPlanExecApiInstance.genArithmeticTransformer(
@@ -612,7 +612,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           a,
-          ExpressionNames.CHECK_MULTIPLY
+          ExpressionNames.CHECKED_MULTIPLY
         )
       case a: Divide =>
         BackendsApiManager.getSparkPlanExecApiInstance.genArithmeticTransformer(
@@ -620,7 +620,7 @@ object ExpressionConverter extends SQLConfHelper with Logging {
           replaceWithExpressionTransformerInternal(a.left, attributeSeq, expressionsMap),
           replaceWithExpressionTransformerInternal(a.right, attributeSeq, expressionsMap),
           a,
-          ExpressionNames.CHECK_DIVIDE
+          ExpressionNames.CHECKED_DIVIDE
         )
       case tryEval: TryEval =>
         // This is a placeholder to handle try_eval(other expressions).
diff --git a/shims/common/src/main/scala/org/apache/gluten/expression/ExpressionNames.scala b/shims/common/src/main/scala/org/apache/gluten/expression/ExpressionNames.scala
index 2be3fad9d39d..8317e28b58bb 100644
--- a/shims/common/src/main/scala/org/apache/gluten/expression/ExpressionNames.scala
+++ b/shims/common/src/main/scala/org/apache/gluten/expression/ExpressionNames.scala
@@ -83,10 +83,10 @@ object ExpressionNames {
   final val IS_NAN = "isnan"
   final val NANVL = "nanvl"
   final val TRY_EVAL = "try"
-  final val CHECK_ADD = "check_add"
-  final val CHECK_SUBTRACT = "check_subtract"
-  final val CHECK_DIVIDE = "check_divide"
-  final val CHECK_MULTIPLY = "check_multiply"
+  final val CHECKED_ADD = "checked_add"
+  final val CHECKED_SUBTRACT = "checked_subtract"
+  final val CHECKED_DIVIDE = "checked_divide"
+  final val CHECKED_MULTIPLY = "checked_multiply"
 
   // SparkSQL String functions
   final val ASCII = "ascii"