diff --git a/mlir/include/mlir/Dialect/Shape/Transforms/Passes.h b/mlir/include/mlir/Dialect/Shape/Transforms/Passes.h
--- a/mlir/include/mlir/Dialect/Shape/Transforms/Passes.h
+++ b/mlir/include/mlir/Dialect/Shape/Transforms/Passes.h
@@ -43,9 +43,12 @@
 void populateShapeTypeConversionPatterns(
     MLIRContext *ctx, BufferAssignmentTypeConverter &converter,
     OwningRewritePatternList &patterns);
-// Collects a set of patterns to replace tensors as inputs and outputs to shape
-// operations with buffers. This only modifies the shape operations.
-std::unique_ptr<FunctionPass> createShapeTensorToMemrefPass();
+// Bufferizes shape dialect ops.
+//
+// Note that most shape dialect ops must be converted to std before
+// bufferization happens, as they are intended to be bufferized at the std
+// level.
+std::unique_ptr<FunctionPass> createShapeBufferizePass();
 
 //===----------------------------------------------------------------------===//
 // Registration
diff --git a/mlir/include/mlir/Dialect/Shape/Transforms/Passes.td b/mlir/include/mlir/Dialect/Shape/Transforms/Passes.td
--- a/mlir/include/mlir/Dialect/Shape/Transforms/Passes.td
+++ b/mlir/include/mlir/Dialect/Shape/Transforms/Passes.td
@@ -22,8 +22,8 @@
 }
 
 // TODO: Generalize this to allow any type conversions desired.
-def ShapeTensorToMemref : FunctionPass<"shape-tensor-to-memref"> {
-  let summary = "Replace tensors involving shape operations with memrefs";
-  let constructor = "mlir::createShapeTensorToMemrefPass()";
+def ShapeBufferize : FunctionPass<"shape-bufferize"> {
+  let summary = "Bufferize the shape dialect.";
+  let constructor = "mlir::createShapeBufferizePass()";
 }
 #endif // MLIR_DIALECT_SHAPE_TRANSFORMS_PASSES
diff --git a/mlir/lib/Dialect/Shape/Transforms/CMakeLists.txt b/mlir/lib/Dialect/Shape/Transforms/CMakeLists.txt
--- a/mlir/lib/Dialect/Shape/Transforms/CMakeLists.txt
+++ b/mlir/lib/Dialect/Shape/Transforms/CMakeLists.txt
@@ -1,6 +1,6 @@
 add_mlir_dialect_library(MLIRShapeOpsTransforms
   RemoveShapeConstraints.cpp
-  ShapeTypeConversion.cpp
+  ShapeBufferize.cpp
   ShapeToShapeLowering.cpp
 
   ADDITIONAL_HEADER_DIRS
diff --git a/mlir/lib/Dialect/Shape/Transforms/ShapeTypeConversion.cpp b/mlir/lib/Dialect/Shape/Transforms/ShapeBufferize.cpp
rename from mlir/lib/Dialect/Shape/Transforms/ShapeTypeConversion.cpp
rename to mlir/lib/Dialect/Shape/Transforms/ShapeBufferize.cpp
--- a/mlir/lib/Dialect/Shape/Transforms/ShapeTypeConversion.cpp
+++ b/mlir/lib/Dialect/Shape/Transforms/ShapeBufferize.cpp
@@ -1,4 +1,4 @@
-//====----- ShapeTypeConversion.cpp - Shape Type Conversions ----*- C++-*--===//
+//====----- ShapeBufferize.cpp - Bufferization of shape ops  ----*- C++-*--===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
@@ -6,8 +6,7 @@
 //
 //===----------------------------------------------------------------------===//
 //
-// This file defines patterns to convert types of inputs and outputs to shape
-// operations to be memrefs instead of tensors.
+// This file defines a bufferization pass for the shape dialect.
 //
 //===----------------------------------------------------------------------===//
 
@@ -53,8 +52,7 @@
   }
 };
 
-struct ShapeTensorToMemrefPass
-    : public ShapeTensorToMemrefBase<ShapeTensorToMemrefPass> {
+struct ShapeBufferizePass : public ShapeBufferizeBase<ShapeBufferizePass> {
   void runOnFunction() override {
     MLIRContext &ctx = getContext();
 
@@ -87,9 +85,9 @@
 }
 
 //===----------------------------------------------------------------------===//
-// ShapeTensorToMemrefPass construction
+// ShapeBufferizePass construction
 //===----------------------------------------------------------------------===//
 
-std::unique_ptr<FunctionPass> mlir::createShapeTensorToMemrefPass() {
-  return std::make_unique<ShapeTensorToMemrefPass>();
+std::unique_ptr<FunctionPass> mlir::createShapeBufferizePass() {
+  return std::make_unique<ShapeBufferizePass>();
 }
diff --git a/mlir/test/Dialect/Shape/shape-type-conversion.mlir b/mlir/test/Dialect/Shape/bufferize.mlir
rename from mlir/test/Dialect/Shape/shape-type-conversion.mlir
rename to mlir/test/Dialect/Shape/bufferize.mlir
--- a/mlir/test/Dialect/Shape/shape-type-conversion.mlir
+++ b/mlir/test/Dialect/Shape/bufferize.mlir
@@ -1,4 +1,4 @@
-// RUN: mlir-opt -split-input-file -shape-tensor-to-memref <%s | FileCheck %s
+// RUN: mlir-opt -split-input-file -shape-bufferize <%s | FileCheck %s
 
 // -----
 // Check that shape.assuming returns a memref.
@@ -14,5 +14,3 @@
   "test.sink"(%1) : (tensor<2xf16>) -> ()
   return
 }
-
-