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>

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