Is it possible to use the Maps app to save a location and give it a name so that all the saved locations appear as a layer?
It's possible to create a personal layer in Google Maps and have it show up in the Maps app. You can create a pin, and label it. However, you will only see pins on the app. But once you click on the pin, you will see your custom text.

Google Maps site. Log-in to Google Maps in Desktop mode (a PC maybe?). At the top left beside the Get directions button, click the My Places button. Then, click the red Create Map button. Give your map a title, add some pins (and custom text) on it, then click the Done button.

Google Maps app. If the app is open, close it and open it again. Once open, click the Layers button at the bottom right. Click My Maps and your list of custom maps will show up, together with the pins you put up. 

See if that's a suitable workaround.

Update: The My Maps option of Google Maps has been discontinued. As of 12th December 2013, a new app, the Google Maps Engine android app has features similar to My Maps option that allows you to create maps from the Google Maps Engine site. This app lets you see it the created maps and layers.