There doesn't appear to be any way to add custom location labels to the current incarnation of Google Maps (Android and Desktop) and it is driving me nuts. It is not just that I miss being able to give saved locations friendly names like "Uncle John's place" or "My Golf Club". It is also that there are loads of places which the current version of maps doesn't seem to be able to provide any address for at all. These include the tennis club I bring my daughter to and the headquarters of a major company that I visited this morning. Not only does Google not know where these places are. It has no mechanism of addressing them because they do not appear on a standard road with a standard building number. I live in a major city in which Google employs several thousand people and this is still an issue here. I can only imagine it is a complete deal breaker for those living in rural locations where every address is something like "The cottage beside Murphy's farm in Hackett's Town".
It is possible to drop a pin on an arbitrary location and save it but you cannot put labels on saved pins which makes them effectively useless. Good luck trying to sort through your saved locations when all you have to go on is a list of 32 digit grid references.
Bizarrely these locations appear in my Google Chrome bookmarks and it is possible to put a label on them in Chrome. That label doesn't appear to transfer across to Google maps though so it is a kludgey work around at best.
The most annoying thing about all of this is that Google Maps used to allow you store your own places. I am sure that Google had their own inscrutable reasons for removing this feature. It might be something to do with their grand plan to move everyone towards Google+ but even though I have completely immersed myself in the Google eco-system I cannot find a way to restore this basic functionality.
This annoys me so much that I have started to look for an alternative mapping solution, hopefully still a free one. There are several out there although some of them seem to be no more than crude overlays on top of Google maps. The best of the bunch seems to be Open Street Map which has desktop and Mobile incarnations. It does have the slightly unfinished "hacker" feel of many open source projects but the navigation tool works very well and their map database seems very complete. I have to spend a bit longer with it to decide whether the added flexibility makes up for the lack of polish.