Waze HQ is working on server upgrades, but I'm seeing about a week cycle right now on the NA (www) server. Please note, that in my working with Waze, it appears that city processing is not done as often as just street updates. Which kinda makes sense from a "where can we save processing time" point of view. The city names and boundaries are really a cosmetic thing, the routing server uses the city names assigned to the road segments, so it's not as critical to update city locations on a daily basis (once the map is up 2 date, the city boundaries shouldn't change that much)

How long does it usually take to updated the map?
I remember I have edited the streets in that area last week. Is it long enough?

How long have you waited since you updated the city names? Things are taking a while to update now, I'm thinking maybe you just haven't waited long enough.