diff --git a/lib/cli/story.js b/lib/cli/story.js
new file mode 100644
index 000000000000..2a64488eda19
--- /dev/null
+++ b/lib/cli/story.js
@@ -0,0 +1,10 @@
+export default {
+  title: 'Story',
+};
+
+export const startCase = () => 'foo';
+export const camelCase = () => 'foo';
+
+camelCase.story = {
+  name: 'camelCase',
+};
diff --git a/lib/codemod/package.json b/lib/codemod/package.json
index b0b3b262dc98..9dc73c93697d 100644
--- a/lib/codemod/package.json
+++ b/lib/codemod/package.json
@@ -23,6 +23,7 @@
   "dependencies": {
     "@mdx-js/mdx": "^1.0.0",
     "@storybook/node-logger": "5.2.1",
+    "@storybook/router": "5.2.1",
     "core-js": "^3.0.1",
     "cross-spawn": "^6.0.5",
     "globby": "^10.0.1",
diff --git a/lib/codemod/src/lib/utils.js b/lib/codemod/src/lib/utils.js
index 822774440a20..4d782569a215 100644
--- a/lib/codemod/src/lib/utils.js
+++ b/lib/codemod/src/lib/utils.js
@@ -9,5 +9,9 @@ export const sanitizeName = name => {
   if (isReserved(key)) {
     key = `${key}Story`;
   }
+  // prepend _ if name starts with a digit
+  if (/^\d/.test(key)) {
+    key = `_${key}`;
+  }
   return key;
 };
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.input.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.input.js
index 459203a04290..17c8f6abc1a1 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.input.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.input.js
@@ -14,4 +14,5 @@ storiesOf('Button', module)
       <br />
     </div>
   ))
-  .add('w/punctuation', () => <Button label="Story 2" onClick={action('click')} />);
+  .add('w/punctuation', () => <Button label="Story 2" onClick={action('click')} />)
+  .add('Start Case', () => <Button label="Story 2" onClick={action('click')} />);
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.output.js
index f5e86149cc1b..a678481c0470 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.output.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/basic.output.js
@@ -10,6 +10,11 @@ export default {
 };
 
 export const story1 = () => <Button label="Story 1" />;
+
+story1.story = {
+  name: 'story1',
+};
+
 export const secondStory = () => <Button label="Story 2" onClick={action('click')} />;
 
 secondStory.story = {
@@ -32,3 +37,5 @@ export const wPunctuation = () => <Button label="Story 2" onClick={action('click
 wPunctuation.story = {
   name: 'w/punctuation',
 };
+
+export const startCase = () => <Button label="Story 2" onClick={action('click')} />;
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.input.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.input.js
index 72e64decea85..232cce44a42a 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.input.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.input.js
@@ -1,2 +1,11 @@
 export const foo = 1;
-storiesOf('bar', module).add('foo', () => <button />);
+const bar = 1;
+const barStory = 1;
+const baz = 1;
+const bazStory1 = 1;
+
+storiesOf('foo', module)
+  .add('foo', () => <button />)
+  .add('bar', () => <button />)
+  .add('bazStory', () => <button />)
+  .add('baz', () => <button />);
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.output.js
index d1300c5bd14f..86f83d12732e 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.output.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/collision.output.js
@@ -1,12 +1,34 @@
 export const foo = 1;
+const bar = 1;
+const barStory = 1;
+const baz = 1;
+const bazStory1 = 1;
 
 export default {
-  title: 'bar',
+  title: 'foo',
   excludeStories: ['foo'],
 };
 
-export const story0 = () => <button />;
+export const fooStory = () => <button />;
 
-story0.story = {
+fooStory.story = {
   name: 'foo',
 };
+
+export const barStory1 = () => <button />;
+
+barStory1.story = {
+  name: 'bar',
+};
+
+export const bazStory = () => <button />;
+
+bazStory.story = {
+  name: 'bazStory',
+};
+
+export const bazStory2 = () => <button />;
+
+bazStory2.story = {
+  name: 'baz',
+};
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.input.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.input.js
new file mode 100644
index 000000000000..9931f13df1f9
--- /dev/null
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.input.js
@@ -0,0 +1 @@
+storiesOf('bar', module).add('1', () => <button />);
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.output.js
new file mode 100644
index 000000000000..0dfb48fb260d
--- /dev/null
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/digit.output.js
@@ -0,0 +1,5 @@
+export default {
+  title: 'bar',
+};
+
+export const _1 = () => <button />;
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/exports.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/exports.output.js
index 8cf839c793e3..57f84925325f 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/exports.output.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/exports.output.js
@@ -6,3 +6,7 @@ export default {
 };
 
 export const baz = () => <button />;
+
+baz.story = {
+  name: 'baz',
+};
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/multi.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/multi.output.js
index ff1fefb3d2b9..588710a8a59f 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/multi.output.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/multi.output.js
@@ -7,11 +7,29 @@ export default {
 };
 
 export const story1 = () => <Button label="Button1.1" />;
+
+story1.story = {
+  name: 'story1',
+};
+
 export const story2 = () => <Button label="Button1.2" />;
 
+story2.story = {
+  name: 'story2',
+};
+
 export default {
   title: 'Button2',
 };
 
-export const story1 = () => <Button label="Button2.1" />;
-export const story2 = () => <Button label="Button2.2" />;
+export const story1Story = () => <Button label="Button2.1" />;
+
+story1Story.story = {
+  name: 'story1',
+};
+
+export const story2Story = () => <Button label="Button2.2" />;
+
+story2Story.story = {
+  name: 'story2',
+};
diff --git a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/story-parameters.output.js b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/story-parameters.output.js
index 6d0b9a5afe40..9aedd776c4f4 100644
--- a/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/story-parameters.output.js
+++ b/lib/codemod/src/transforms/__testfixtures__/storiesof-to-csf/story-parameters.output.js
@@ -20,6 +20,8 @@ withStoryParameters.story = {
 export const foo = () => <Button label="Foo" />;
 
 foo.story = {
+  name: 'foo',
+
   parameters: {
     bar: 1,
   },
diff --git a/lib/codemod/src/transforms/__tests__/storiesof-to-csf.test.js b/lib/codemod/src/transforms/__tests__/storiesof-to-csf.test.js
index 73c8b6486894..05f60dd9e769 100644
--- a/lib/codemod/src/transforms/__tests__/storiesof-to-csf.test.js
+++ b/lib/codemod/src/transforms/__tests__/storiesof-to-csf.test.js
@@ -1,21 +1,14 @@
+import fs from 'fs';
+import path from 'path';
+
 import { defineTest } from 'jscodeshift/dist/testUtils';
 
 jest.mock('@storybook/node-logger');
 
-const testNames = [
-  'basic',
-  'decorators',
-  'parameters',
-  'story-parameters',
-  'module',
-  'multi',
-  'default',
-  'exports',
-  'collision',
-  'const',
-  'story-decorators',
-];
-
-testNames.forEach(testName => {
-  defineTest(__dirname, `storiesof-to-csf`, null, `storiesof-to-csf/${testName}`);
-});
+fs.readdirSync(path.resolve(__dirname, '../__testfixtures__/storiesof-to-csf'))
+  .map(filename => filename.match(/^(.*)\.input\.js$/))
+  .filter(Boolean)
+  .map(match => match[1])
+  .forEach(testName => {
+    defineTest(__dirname, `storiesof-to-csf`, null, `storiesof-to-csf/${testName}`);
+  });
diff --git a/lib/codemod/src/transforms/storiesof-to-csf.js b/lib/codemod/src/transforms/storiesof-to-csf.js
index 1fe45368471b..fca733b0a405 100644
--- a/lib/codemod/src/transforms/storiesof-to-csf.js
+++ b/lib/codemod/src/transforms/storiesof-to-csf.js
@@ -1,5 +1,6 @@
 import prettier from 'prettier';
 import { logger } from '@storybook/node-logger';
+import { storyNameFromExport } from '@storybook/router';
 import { sanitizeName } from '../lib/utils';
 
 /**
@@ -44,7 +45,7 @@ export default function transformer(file, api, options) {
     return { storyParams, storyDecorators };
   }
 
-  function convertToModuleExports(path, originalExports, counter) {
+  function convertToModuleExports(path, originalExports) {
     const base = j(path);
 
     const statements = [];
@@ -127,13 +128,19 @@ export default function transformer(file, api, options) {
     adds.reverse();
     adds.push(path);
 
+    const identifiers = new Set();
+    root.find(j.Identifier).forEach(({ value }) => identifiers.add(value.name));
     adds.forEach(add => {
       let name = add.node.arguments[0].value;
-      let key = sanitizeName(name);
-      if (originalExports.includes(key)) {
-        key = `story${counter}`;
+      const sanitized = sanitizeName(name);
+      let key = sanitized;
+      let counter = 0;
+      while (identifiers.has(key)) {
+        key = `${sanitized}Story${counter || ''}`;
+        counter += 1;
       }
-      if (key === name) {
+      identifiers.add(key);
+      if (storyNameFromExport(key) === name) {
         name = null;
       }
 
@@ -209,7 +216,7 @@ export default function transformer(file, api, options) {
     .filter(add => add.node.callee.property && add.node.callee.property.name === 'add')
     .filter(add => add.node.arguments.length >= 2 && add.node.arguments[0].type === 'Literal')
     .filter(add => add.parentPath.node.type === 'ExpressionStatement')
-    .forEach((path, i) => convertToModuleExports(path, originalExports, i));
+    .forEach(path => convertToModuleExports(path, originalExports));
 
   // remove storiesOf import
   root