A shop can be renamed and, while empty, removed - from head office

The display name was always meant to be editable and the slug frozen;
until now neither had a way in. PATCH /api/sites/{site} takes a name
and a timezone (manager and above), DELETE removes an empty shop
(owner). The shop drawer in head office gets both, with the short name
shown read-only and the reason beside it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01KGcjxF1cNLcuwc3DAPcnfj

server/internal/api/fake_test.go

@@ -554,6 +554,23 @@ func (f *fakeStore) DeleteClient(_ context.Context, clientID string) (ClientRow,
 	return ClientRow{}, nil, pgx.ErrNoRows
 }
 
+func (f *fakeStore) UpdateSite(_ context.Context, _ string, siteID string, in SiteUpdate) (SiteHealth, error) {
+	f.mu.Lock()
+	defer f.mu.Unlock()
+	for i := range f.sites {
+		if f.sites[i].SiteID == siteID {
+			if in.Name != nil {
+				f.sites[i].Name = *in.Name
+			}
+			if in.Timezone != nil {
+				f.sites[i].Timezone = *in.Timezone
+			}
+			return f.sites[i], nil
+		}
+	}
+	return SiteHealth{}, pgx.ErrNoRows
+}
+
 func (f *fakeStore) DeleteEmptySite(_ context.Context, _ string, siteID string) (string, error) {
 	f.mu.Lock()
 	defer f.mu.Unlock()