We made some modifications to the zone lookup app to add additional capabilities. One of these is that the results are grouped by layer. If you want to disable this behavior you can turn off the "Group results by layer" option in the app configuration.
If this doesn't seem to resolve the issue and your app is public can you send me the link? If its not public can you share a screenshot showing what you are seeing?
If I look at the web map json it looks like the layer names match those shown in the app. Here's a screen shot showing the title of the layer is District_Locator_05202021 - COGS. If you open your web map in the Map Viewer do you still see your custom layer titles?