diff --git a/mlir/lib/Target/LLVMIR/TypeFromLLVM.cpp b/mlir/lib/Target/LLVMIR/TypeFromLLVM.cpp
--- a/mlir/lib/Target/LLVMIR/TypeFromLLVM.cpp
+++ b/mlir/lib/Target/LLVMIR/TypeFromLLVM.cpp
@@ -112,14 +112,13 @@
     if (type->isOpaque())
       return LLVM::LLVMStructType::getOpaque(type->getName(), &context);
 
-    LLVM::LLVMStructType translated =
-        LLVM::LLVMStructType::getIdentified(&context, type->getName());
-    knownTranslations.try_emplace(type, translated);
+    // With opaque pointers, types in LLVM can't be recursive anymore. Note that
+    // using getIdentified is not possible, as type names in LLVM are not
+    // guaranteed to be unique.
     translateTypes(type->subtypes(), subtypes);
-    LogicalResult bodySet = translated.setBody(subtypes, type->isPacked());
-    assert(succeeded(bodySet) &&
-           "could not set the body of an identified struct");
-    (void)bodySet;
+    LLVM::LLVMStructType translated = LLVM::LLVMStructType::getNewIdentified(
+        &context, type->getName(), subtypes, type->isPacked());
+    knownTranslations.try_emplace(type, translated);
     return translated;
   }
 
diff --git a/mlir/test/Target/LLVMIR/Import/global-struct.ll b/mlir/test/Target/LLVMIR/Import/global-struct.ll
new file mode 100644
--- /dev/null
+++ b/mlir/test/Target/LLVMIR/Import/global-struct.ll
@@ -0,0 +1,8 @@
+; RUN: mlir-translate --import-llvm %s | FileCheck %s
+
+; Ensure both structs have different names.
+; CHECK: llvm.func @fn(!llvm.struct<"[[NAME:[^"]*]]",
+; CHECK-NOT: struct<"[[NAME]]",
+%0 = type { %1 }
+%1 = type { i8 }
+declare void @fn(%0)