For quite a few years I lived near and worked in the San Fernando Valley area of Los Angeles. Probably 3/4 of the postal cities there are simply named areas within the City of Los Angeles. I think only San Fernando, Burbank, Calabasas and maybe Hidden Hills are separate cities. Glendale is a separate city but only really touches the SF Valley. All the others, places like Studio City, Van Nuys, Tarzana, Woodland Hills, Chatworth, Northridge, Granda Hills, etc. are all officially just parts of the large city of LA.
But the USPS and locals, news media, etc. use those local names. LA is “over the hill” from “The Valley” and you’d never give directions, mail, or ship (USPS, FedEx, UPS, etc.) with LA as the city in the address field.
So I’d put the postal name in the addr:city field.
Corollary to that is the addr:city value should be one of the USPS recognized values for the ZIP code.
For what it is worth, our current house was once a duplex and when we moved in we received a lot of mail to “Unit A” and/or “Unit B”. And we had some mail order forms that insisted we give them a unit or apartment number.
I went to the post office to get our address information corrected. I was told they get their data from the county. And on further investigation, it turns out that for incorporated cities, the county gets address data from the city. This leads me to believe that, at least in Orange County in California, the 911 address likely matches the city, county, and for my area, USPS address.
Years later we still occasionally get mail to Unit A or Unit B but at least now we are not forced to add a fictitious unit number to an Internet purchase form. Amazing how long it takes for corrections to percolate through various databases.