diff --git a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
--- a/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
+++ b/mlir/lib/Dialect/SparseTensor/Transforms/SparseTensorCodegen.cpp
@@ -486,7 +486,7 @@
                                    StringRef namePrefix,
                                    FuncGeneratorType createFunc) {
   // The mangled name of the function has this format:
-  //   <namePrefix>_[C|S|D]_<shape>_<ordering>_<eltType>
+  //   <namePrefix>_[C|S|D][NU]_<shape>_<ordering>_<eltType>
   //     _<indexBitWidth>_<pointerBitWidth>
   RankedTensorType rtp = desc.getTensorType();
   SmallString<32> nameBuffer;
@@ -496,12 +496,16 @@
   assert(rank == indices.size());
   for (unsigned d = 0; d < rank; d++) {
     if (isCompressedDim(rtp, d)) {
-      nameOstream << "C_";
+      nameOstream << "C";
     } else if (isSingletonDim(rtp, d)) {
-      nameOstream << "S_";
+      nameOstream << "S";
     } else {
-      nameOstream << "D_";
+      nameOstream << "D";
     }
+    if (isUniqueDim(rtp, d))
+      nameOstream << "_";
+    else
+      nameOstream << "NU_";
   }
   // Static dim sizes are used in the generated code while dynamic sizes are
   // loaded from the dimSizes buffer. This is the reason for adding the shape
diff --git a/mlir/test/Dialect/SparseTensor/codegen.mlir b/mlir/test/Dialect/SparseTensor/codegen.mlir
--- a/mlir/test/Dialect/SparseTensor/codegen.mlir
+++ b/mlir/test/Dialect/SparseTensor/codegen.mlir
@@ -46,6 +46,10 @@
   dimOrdering = affine_map<(i, j, k) -> (k, i, j)>
 }>
 
+#Coo = #sparse_tensor.encoding<{
+  dimLevelType = [ "compressed-nu", "singleton" ]
+}>
+
 // CHECK-LABEL: func @sparse_nop(
 //  CHECK-SAME: %[[A0:.*0]]: memref<1xindex>,
 //  CHECK-SAME: %[[A1:.*1]]: memref<3xindex>,
@@ -594,6 +598,37 @@
   return %1 : tensor<128xf64, #SparseVector>
 }
 
+// CHECK-LABEL: func.func private @_insert_CNU_S_5_6_f64_0_0(
+//  CHECK-SAME: %[[A0:.*0]]: memref<2xindex>,
+//  CHECK-SAME: %[[A1:.*1]]: memref<4xindex>,
+//  CHECK-SAME: %[[A2:.*2]]: memref<?xindex>,
+//  CHECK-SAME: %[[A3:.*3]]: memref<?xindex>,
+//  CHECK-SAME: %[[A4:.*4]]: memref<?xindex>,
+//  CHECK-SAME: %[[A5:.*5]]: memref<?xf64>,
+//  CHECK-SAME: %[[A6:.*6]]: index,
+//  CHECK-SAME: %[[A7:.*7]]: index,
+//  CHECK-SAME: %[[A8:.*8]]: f64)
+//       CHECK: %[[P0:.*]] = sparse_tensor.push_back %[[A1]], %[[A3]], %[[A6]]
+//       CHECK: %[[P1:.*]] = sparse_tensor.push_back %[[A1]], %[[A4]], %[[A7]]
+//       CHECK: %[[P2:.*]] = sparse_tensor.push_back %[[A1]], %[[A5]], %[[A8]]
+//       CHECK: return %[[A0]], %[[A1]], %[[A2]], %[[P0]], %[[P1]], %[[P2]]
+//       CHECK: func.func @sparse_insert_coo(
+//  CHECK-SAME: %[[A0:.*0]]: memref<2xindex>,
+//  CHECK-SAME: %[[A1:.*1]]: memref<4xindex>,
+//  CHECK-SAME: %[[A2:.*2]]: memref<?xindex>,
+//  CHECK-SAME: %[[A3:.*3]]: memref<?xindex>,
+//  CHECK-SAME: %[[A4:.*4]]: memref<?xindex>,
+//  CHECK-SAME: %[[A5:.*5]]: memref<?xf64>,
+//  CHECK-SAME: %[[A6:.*6]]: index,
+//  CHECK-SAME: %[[A7:.*7]]: f64)
+//       CHECK: %[[R:.*]]:6 = call @_insert_CNU_S_5_6_f64_0_0(%[[A0]], %[[A1]], %[[A2]], %[[A3]], %[[A4]], %[[A5]], %[[A6]], %[[A6]], %[[A7]])
+//       CHECK: return %[[R]]#0, %[[R]]#1, %[[R]]#2, %[[R]]#3, %[[R]]#4, %[[R]]#5
+func.func @sparse_insert_coo(%arg0: tensor<5x6xf64, #Coo>, %arg1: index, %arg2: f64) -> tensor<5x6xf64, #Coo> {
+  %0 = sparse_tensor.insert %arg2 into %arg0[%arg1, %arg1] : tensor<5x6xf64, #Coo>
+  %1 = sparse_tensor.load %0 hasInserts : tensor<5x6xf64, #Coo>
+  return %1 : tensor<5x6xf64, #Coo>
+}
+
 // CHECK-LABEL: func.func @sparse_nop_convert(
 //  CHECK-SAME: %[[A0:.*0]]: memref<1xindex>,
 //  CHECK-SAME: %[[A1:.*1]]: memref<3xindex>,