My first thought is that Mirrorith is a complicated name to say. I'd bet that rapidly people would be mispronouncing it to something more like "Mrith" or even just "'Rith" - most populous cities have fairly short names because they are names that people use the whole time.
Onto the point - how do neighbourhoods get their names?
In a large city, many of them started out as separate towns or villages - if you look at historical maps of London it is very clear how the city has grown and swallowed up previously separate villages or towns giving us Hackney, Camberwell, Clapham and Streatham, all of which are fairly typical English Town names.
London ( it's my local capital city so I will tend towards it for examples ) has quite a few areas whose names are actually just the name of the land the city swallowed up - Blackheath and Shepherds Bush - or the name of a significant building in the area - Westminster, Crystal Palace. There is a common process where one might start off with a topographic name and then later the language may change or be superseded by an invador's tongue so the name becomes less obvious. A good example of this might be equivalent names- Dublin and Blackpool are very similar in terms of what they describe, in different languages.
Sometimes neighbourhoods are named for their functions but this tends to be restricted to relatively significante areas - docks tend to name their immediate areas, in particular, but it is relatively unusual beyond that. You are more likely to see street names that reflect the trades in an area ( "Tanners Row", "Smith Street" ) than you are to see an entire area named after a particular area.
Sometimes place names are related to a particular demographic- for example one could probably guess the relative affluence of Cheapside and Covent Garden when they were named. Different social classes are likely to have quite different environments and so names reflecting parks, gardens and other relatively leisurely pastimes are more likely to arise in affluent areas, whereas names indicating population density or industrial activity are likely to be less affluent.
Regardless of how you name your districts, remember that names are things that people use constantly. As a result they get worn to convenient shapes. If different social elements in your setting have different accents, then the names will- to a degree- shape to fit into those accents. Names tend to get shorter and lose syllables because it's more convenient to say them that way, but most towns also have a few names that are slighly hard to pronounce, with which locals delight in making it hard for outsiders to follow directions.