Implement task 6.1: Create PUT /api/auth/profile endpoint for updating user display name

- Create src/app/api/auth/profile/route.ts with PUT handler
- Validates user is authenticated (returns 401 if not)
- Validates request body has a non-empty name field
- Updates user's name in the database
- Returns 200 with updated user data

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

drizzle/meta/_journal.json

@@ -8,6 +8,13 @@
       "when": 1771332001387,
       "tag": "0000_nifty_gauntlet",
       "breakpoints": true
+    },
+    {
+      "idx": 1,
+      "version": "7",
+      "when": 1771577402984,
+      "tag": "0001_daffy_zaladane",
+      "breakpoints": true
     }
   ]
 }