Remove Display Name field from user profile settings

Username is the only user-facing name field. The display_name column
remains in the database since BetterAuth writes the OAuth provider name
there, and it serves as a programmatic fallback via getUserDisplayName.

https://claude.ai/code/session_01NUv93WRrufHhpZSMyY4bjs

app/components/user/settings/ProfileSection.tsx

@@ -39,7 +39,7 @@ export function ProfileSection({ user, isInActiveDraft, success, error }: Props)
       <div>
         <h2 className="text-lg font-semibold">Profile</h2>
         <p className="text-sm text-muted-foreground">
-          Your display name, username, avatar, and timezone.
+          Your username, avatar, and timezone.
         </p>
       </div>
 
@@ -58,14 +58,6 @@ export function ProfileSection({ user, isInActiveDraft, success, error }: Props)
       </div>
 
       <Form method="post" className="space-y-4">
-        <div className="space-y-2">
-          <Label htmlFor="displayName">Display Name</Label>
-          <Input
-            id="displayName"
-            name="displayName"
-            defaultValue={user.displayName ?? ""}
-          />
-        </div>
         <div className="space-y-2">
           <Label htmlFor="username">Username</Label>
           <Input

app/routes/settings.tsx

@@ -118,12 +118,10 @@ export async function action(args: Route.ActionArgs): Promise<ActionData | Respo
   }
 
   if (intent === "update-profile") {
-    const displayName = formData.get("displayName") as string;
     const username = formData.get("username") as string | null;
     const timezone = formData.get("timezone") as string | null;
     const timezoneValue = timezone && VALID_TIMEZONES.has(timezone) ? timezone : undefined;
     await updateUser(session.user.id, {
-      displayName: displayName || undefined,
       username: username || undefined,
       timezone: timezoneValue,
     });