Wow, my jaw is on the floor because of a huge, but sorely lacking feature in this app: the ability to edit the name of a starred location. This isn't a problem if I want to star "Steve's Pizza" since that's how it shows up in their directory, but what about my grandmother's house? I can star her location, sure, but it'll appear in the search history list as a random address once it's one of many other such entries. Am I wrong to think this is a massive oversight over a common use-case? Let's put the Google praise parade on hold and reflect on this for a second.
TL;DR You can't edit the name of your starred locations from the iOS Google Maps app.
Doesn't seem like a 'massive oversight' to me. Definitely a 'should have' feature, but not something that needed to be in this release from an MVP perspective.
This was one of the first things I noticed as well. It seems like such basic functionality (the maps app in iOS had this since at least iOS3), I was amazed to find you can't edit them in the app (thankfully you can see @andrewaylett's comment for a way to do it).
There are several serious bugs in the saved locations functionality.
I found that if you 'pin' a location (say a building) on the map (by pressing and holding) it will show the address. But when you 'save' it, the details of the address get 'lost' when looking at your search history. I ended up with multiple entries in my list titled 'Shinjuku, Tokyo, Japan' (which is the equivalent of, say, 'Manhatten, New York, USA'. Clicking each one still takes you to the correct location on the map, but they are impossible to tell apart in the list. Also then when using the 'directions' widget on the map and picking the destination, these saved locations appeared as longitude/latitude!
I wonder if these issues are specific to Japan? I submitted feedback about this.
That being said, overall the app is quite impressive, and I'm sure it will improve.
You can't do this from the Android version either, it's an annoying oversight. I've resorted to taking all important locations and putting them into a custom map; the location markers in custom maps /can/ be named.
TL;DR You can't edit the name of your starred locations from the iOS Google Maps app.