diff --git a/lld/test/wasm/strip-debug.test b/lld/test/wasm/strip-debug.test
--- a/lld/test/wasm/strip-debug.test
+++ b/lld/test/wasm/strip-debug.test
@@ -6,5 +6,5 @@
 RUN: wasm-ld -S -o %t.wasm %t.start.o
 RUN: obj2yaml %t.wasm | FileCheck %s
 
-# Check that there is no name section
-CHECK-NOT:   Name:    name
+# Check that there is a name section
+CHECK:   Name:    name
diff --git a/lld/test/wasm/weak-undefined.s b/lld/test/wasm/weak-undefined.s
--- a/lld/test/wasm/weak-undefined.s
+++ b/lld/test/wasm/weak-undefined.s
@@ -1,5 +1,5 @@
 # RUN: llvm-mc -filetype=obj -triple=wasm32-unknown-unknown -o %t.o %s
-# RUN: wasm-ld -strip-debug %t.o -o %t.wasm
+# RUN: wasm-ld -strip-all %t.o -o %t.wasm
 # RUN: obj2yaml %t.wasm | FileCheck %s
 
 # Test that undefined weak externals (global_var) and (foo) don't cause
diff --git a/lld/wasm/SyntheticSections.h b/lld/wasm/SyntheticSections.h
--- a/lld/wasm/SyntheticSections.h
+++ b/lld/wasm/SyntheticSections.h
@@ -362,9 +362,7 @@
   NameSection(ArrayRef<OutputSegment *> segments)
       : SyntheticSection(llvm::wasm::WASM_SEC_CUSTOM, "name"),
         segments(segments) {}
-  bool isNeeded() const override {
-    return !config->stripDebug && !config->stripAll && numNames() > 0;
-  }
+  bool isNeeded() const override { return !config->stripAll && numNames() > 0; }
   void writeBody() override;
   unsigned numNames() const { return numNamedGlobals() + numNamedFunctions(); }
   unsigned numNamedGlobals() const;