fix(auth): allow registration without display name

apps/api/app/api/routes/auth.py

@@ -5,6 +5,8 @@ The route layer is intentionally thin: repository construction lives in
 app.dependencies and authentication behavior lives in application use cases.
 """
 
+from typing import Optional
+
 from app.auth import AuthenticatedUser, get_current_user
 from app.config import settings
 from app.dependencies import get_auth_email_service, get_auth_session_store, get_user_repository
@@ -32,7 +34,7 @@ class RegisterRequest(BaseModel):
     email: EmailStr
     password: str
     username: str
-    display_name: str
+    display_name: Optional[str] = None
 
 
 class RegisterResponse(BaseModel):
@@ -99,7 +101,7 @@ async def register(
             email=request.email,
             password=request.password,
             username=request.username,
-            display_name=request.display_name,
+            display_name=request.display_name or request.username,
         )
     )
     if error or response is None: