diff --git a/llvm/include/llvm/Object/Wasm.h b/llvm/include/llvm/Object/Wasm.h
--- a/llvm/include/llvm/Object/Wasm.h
+++ b/llvm/include/llvm/Object/Wasm.h
@@ -287,7 +287,6 @@
   uint32_t StartFunction = -1;
   bool HasLinkingSection = false;
   bool HasDylinkSection = false;
-  bool SeenCodeSection = false;
   bool HasMemory64 = false;
   wasm::WasmLinkingData LinkingData;
   uint32_t NumImportedGlobals = 0;
diff --git a/llvm/lib/Object/WasmObjectFile.cpp b/llvm/lib/Object/WasmObjectFile.cpp
--- a/llvm/lib/Object/WasmObjectFile.cpp
+++ b/llvm/lib/Object/WasmObjectFile.cpp
@@ -451,10 +451,6 @@
   llvm::DenseSet<uint64_t> SeenFunctions;
   llvm::DenseSet<uint64_t> SeenGlobals;
   llvm::DenseSet<uint64_t> SeenSegments;
-  if (Functions.size() && !SeenCodeSection) {
-    return make_error<GenericBinaryError>("names must come after code section",
-                                          object_error::parse_failed);
-  }
 
   while (Ctx.Ptr < Ctx.End) {
     uint8_t Type = readUint8(Ctx);
@@ -474,7 +470,7 @@
             return make_error<GenericBinaryError>(
                 "function named more than once", object_error::parse_failed);
           if (!isValidFunctionIndex(Index) || Name.empty())
-            return make_error<GenericBinaryError>("invalid name entry",
+            return make_error<GenericBinaryError>("invalid function name entry",
                                                   object_error::parse_failed);
 
           if (isDefinedFunctionIndex(Index))
@@ -485,7 +481,7 @@
             return make_error<GenericBinaryError>("global named more than once",
                                                   object_error::parse_failed);
           if (!isValidGlobalIndex(Index) || Name.empty())
-            return make_error<GenericBinaryError>("invalid name entry",
+            return make_error<GenericBinaryError>("invalid global name entry",
                                                   object_error::parse_failed);
         } else {
           nameType = wasm::NameType::DATA_SEGMENT;
@@ -493,7 +489,7 @@
             return make_error<GenericBinaryError>(
                 "segment named more than once", object_error::parse_failed);
           if (Index > DataSegments.size())
-            return make_error<GenericBinaryError>("invalid named data segment",
+            return make_error<GenericBinaryError>("invalid data segment name entry",
                                                   object_error::parse_failed);
         }
         DebugNames.push_back(wasm::WasmDebugName{nameType, Index, Name});
@@ -519,11 +515,6 @@
 
 Error WasmObjectFile::parseLinkingSection(ReadContext &Ctx) {
   HasLinkingSection = true;
-  if (Functions.size() && !SeenCodeSection) {
-    return make_error<GenericBinaryError>(
-        "linking data must come after code section",
-        object_error::parse_failed);
-  }
 
   LinkingData.Version = readVaruint32(Ctx);
   if (LinkingData.Version != wasm::WasmMetadataVersion) {
@@ -1410,7 +1401,6 @@
 }
 
 Error WasmObjectFile::parseCodeSection(ReadContext &Ctx) {
-  SeenCodeSection = true;
   CodeSection = Sections.size();
   uint32_t FunctionCount = readVaruint32(Ctx);
   if (FunctionCount != Functions.size()) {
diff --git a/llvm/test/tools/llvm-objdump/wasm/no-codesec.test b/llvm/test/tools/llvm-objdump/wasm/no-codesec.test
new file mode 100644
--- /dev/null
+++ b/llvm/test/tools/llvm-objdump/wasm/no-codesec.test
@@ -0,0 +1,26 @@
+## Test that sections that use function indices (e.g. name) work without the code section
+# RUN: yaml2obj %s -o %t
+# RUN: llvm-objdump -h %t | FileCheck %s
+
+# CHECK: Sections:
+# CHECK-NEXT: Idx Name          Size     VMA      Type
+# CHECK-NEXT:   0 TYPE          00000004 00000000 
+# CHECK-NEXT:   1 FUNCTION      00000002 00000000 
+# CHECK-NEXT:   2 name          00000008 00000000
+  
+--- !WASM
+FileHeader:
+  Version: 0x00000001
+Sections:
+  - Type: TYPE
+    Signatures:
+      - Index: 0
+        ParamTypes: []
+        ReturnTypes: []
+  - Type: FUNCTION
+    FunctionTypes: [ 0 ]
+  - Type: CUSTOM
+    Name: name
+    FunctionNames:
+     - Index:          0
+       Name:           foo