diff --git a/src/Interpreters/InterpreterCreateFunctionQuery.cpp b/src/Interpreters/InterpreterCreateFunctionQuery.cpp
index ccb5f4040ec..9d92466c440 100644
--- a/src/Interpreters/InterpreterCreateFunctionQuery.cpp
+++ b/src/Interpreters/InterpreterCreateFunctionQuery.cpp
@@ -1,14 +1,17 @@
+#include <Interpreters/InterpreterCreateFunctionQuery.h>
+
+#include <stack>
+
 #include <Access/ContextAccess.h>
 #include <Parsers/ASTCreateFunctionQuery.h>
 #include <Parsers/ASTIdentifier.h>
 #include <Interpreters/Context.h>
 #include <Interpreters/ExpressionActions.h>
 #include <Interpreters/ExpressionAnalyzer.h>
-#include <Interpreters/InterpreterCreateFunctionQuery.h>
 #include <Interpreters/FunctionNameNormalizer.h>
 #include <Interpreters/UserDefinedSQLObjectsLoader.h>
 #include <Interpreters/UserDefinedSQLFunctionFactory.h>
-#include <stack>
+
 
 namespace DB
 {
@@ -66,42 +69,9 @@ void InterpreterCreateFunctionQuery::validateFunction(ASTPtr function, const Str
     }
 
     ASTPtr function_body = function->as<ASTFunction>()->children.at(0)->children.at(1);
-    std::unordered_set<String> identifiers_in_body = getIdentifiers(function_body);
-
-    for (const auto & identifier : identifiers_in_body)
-    {
-        if (!arguments.contains(identifier))
-            throw Exception(ErrorCodes::UNKNOWN_IDENTIFIER, "Identifier {} does not exist in arguments", backQuote(identifier));
-    }
-
     validateFunctionRecursiveness(function_body, name);
 }
 
-std::unordered_set<String> InterpreterCreateFunctionQuery::getIdentifiers(ASTPtr node)
-{
-    std::unordered_set<String> identifiers;
-
-    std::stack<ASTPtr> ast_nodes_to_process;
-    ast_nodes_to_process.push(node);
-
-    while (!ast_nodes_to_process.empty())
-    {
-        auto ast_node_to_process = ast_nodes_to_process.top();
-        ast_nodes_to_process.pop();
-
-        for (const auto & child : ast_node_to_process->children)
-        {
-            auto identifier_name_opt = tryGetIdentifierName(child);
-            if (identifier_name_opt)
-                identifiers.insert(identifier_name_opt.value());
-
-            ast_nodes_to_process.push(child);
-        }
-    }
-
-    return identifiers;
-}
-
 void InterpreterCreateFunctionQuery::validateFunctionRecursiveness(ASTPtr node, const String & function_to_create)
 {
     for (const auto & child : node->children)
diff --git a/src/Interpreters/InterpreterCreateFunctionQuery.h b/src/Interpreters/InterpreterCreateFunctionQuery.h
index fdc03b379db..a67fdb9605d 100644
--- a/src/Interpreters/InterpreterCreateFunctionQuery.h
+++ b/src/Interpreters/InterpreterCreateFunctionQuery.h
@@ -22,7 +22,6 @@ public:
 
 private:
     static void validateFunction(ASTPtr function, const String & name);
-    static std::unordered_set<String> getIdentifiers(ASTPtr node);
     static void validateFunctionRecursiveness(ASTPtr node, const String & function_to_create);
 
     ASTPtr query_ptr;
diff --git a/src/Interpreters/UserDefinedSQLFunctionVisitor.cpp b/src/Interpreters/UserDefinedSQLFunctionVisitor.cpp
index cc5db020387..8df6932b153 100644
--- a/src/Interpreters/UserDefinedSQLFunctionVisitor.cpp
+++ b/src/Interpreters/UserDefinedSQLFunctionVisitor.cpp
@@ -25,6 +25,7 @@ void UserDefinedSQLFunctionMatcher::visit(ASTPtr & ast, Data &)
         return;
 
     auto result = tryToReplaceFunction(*function);
+
     if (result)
         ast = result;
 }
@@ -83,9 +84,16 @@ ASTPtr UserDefinedSQLFunctionMatcher::tryToReplaceFunction(const ASTFunction & f
             if (identifier_name_opt)
             {
                 auto function_argument_it = identifier_name_to_function_argument.find(*identifier_name_opt);
-                assert(function_argument_it != identifier_name_to_function_argument.end());
 
+                if (function_argument_it == identifier_name_to_function_argument.end())
+                    continue;
+
+                auto child_alias = child->tryGetAlias();
                 child = function_argument_it->second->clone();
+
+                if (!child_alias.empty())
+                    child->setAlias(child_alias);
+
                 continue;
             }
 
diff --git a/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.reference b/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.reference
new file mode 100644
index 00000000000..8ab2f6d0ac6
--- /dev/null
+++ b/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.reference
@@ -0,0 +1 @@
+8	4
diff --git a/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.sql b/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.sql
new file mode 100644
index 00000000000..fef2daf8fd1
--- /dev/null
+++ b/tests/queries/0_stateless/02098_sql_user_defined_functions_aliases.sql
@@ -0,0 +1,4 @@
+-- Tags: no-parallel
+CREATE FUNCTION alias_function AS x -> (((x * 2) AS x_doubled) + x_doubled);
+SELECT alias_function(2);
+DROP FUNCTION alias_function;
diff --git a/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.reference b/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.reference
new file mode 100644
index 00000000000..8f6cd5ccd03
--- /dev/null
+++ b/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.reference
@@ -0,0 +1 @@
+[2,4,6]
diff --git a/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.sql b/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.sql
new file mode 100644
index 00000000000..e66651c1e5a
--- /dev/null
+++ b/tests/queries/0_stateless/02099_sql_user_defined_functions_lambda.sql
@@ -0,0 +1,4 @@
+-- Tags: no-parallel
+CREATE FUNCTION lambda_function AS x -> arrayMap(array_element -> array_element * 2, x);
+SELECT lambda_function([1,2,3]);
+DROP FUNCTION lambda_function;