Hi Matt, 
Apologies for the brevity of my earlier message. I saw your edits coming in but didn't have time just then for more constructive criticism. Thanks Jarek for jumping in to fill that gap!

One way I'd suggest thinking about the namelessness here is that these are service roads, and most service roads actually don't have names. Private or semi-private driveways for example very rarely would be named. I wouldn't want to see https://www.openstreetmap.org/way/232723249 for example called "No Frills Driveway" or something like that. Where would it stop? Would the parking aisles have names too? "Easternmost North-South No Frills Parking Aisle" etc

Also, from the perspective of someone potentially using these names/descriptions to help navigate, I would think these would create confusion if anything. There's no indication of these names in physical reality, so if you were expecting that you might think you were in the wrong place. Better to have a direction like "turn left onto the unnamed alley" as an unnamed alley is what you would actually see.

Definitely not writing on behalf of the City by the way; the City has no say over what's right for OSM. Nor does Google Maps or any else for that matter. 

Here's a good rundown of how to use the "name" tag: https://wiki.openstreetmap.org/wiki/Names#Name_is_the_name_only
It appears there's actually a tag to indicate namelessness too https://wiki.openstreetmap.org/wiki/Tag:noname%3Dyes which should probably be added to most of the city's alleys and might help to prevent some confusion in the future. 

Best,
Nate