fix(misc): set project names used the old logic including dirs

(cherry picked from commit 4ba4bd0)

packages/nx/src/migrations/update-15-1-0/set-project-names.ts

@@ -1,6 +1,7 @@
 import { Tree } from '../../generators/tree';
 import {
   getProjects,
+  readNxJson,
   updateProjectConfiguration,
 } from '../../generators/utils/project-configuration';
 import { formatChangedFilesWithPrettierIfAvailable } from '../../generators/internal-utils/format-changed-files-with-prettier-if-available';
@@ -10,10 +11,23 @@ export default async function (tree: Tree) {
   // This looks like it does nothing, but this will actually effectively migrate over all the configs that need to be moved over, but won't touch configs that don't need to be moved
   for (const [projName, projConfig] of getProjects(tree)) {
     if (tree.exists(join(projConfig.root, 'project.json'))) {
-      projConfig.name ??= projName;
+      if (!projConfig.name) {
+        projConfig.name = toProjectName(projConfig.root, readNxJson(tree));
+      }
       updateProjectConfiguration(tree, projName, projConfig);
     }
   }
 
   await formatChangedFilesWithPrettierIfAvailable(tree);
 }
+
+function toProjectName(directory: string, nxJson: any): string {
+  let { appsDir, libsDir } = nxJson?.workspaceLayout || {};
+  appsDir ??= 'apps';
+  libsDir ??= 'libs';
+  const parts = directory.split(/[\/\\]/g);
+  if ([appsDir, libsDir].includes(parts[0])) {
+    parts.splice(0, 1);
+  }
+  return parts.join('-').toLowerCase();
+}