[PHX31]

There aren't many neighborhood designations in the common vernacular. The City has tried fragmenting neighborhoods into names, but I guarantee you no one in the entire metro area knows where "New Village" is located. In general the whole city name is typically used, sometimes with a direction added (ie, South Scottsdale vs North Scottsdale, or South Tempe). There are a few, and I would say these are the most common (disregarding from the historic neighborhoods) :

Neighborhood name / location

Sunnyslope / (north phoenix)
Maryvale / (west phoenix)
Arcadia / (NE central phoenix)
Ahwatukee / (south phoenix on the other side of south mountain)
Anthem / (far far north phoenix)

Then there are some that are possibly less common in the city as a whole, but may be more localized. Some follow housing/development names that are big and may have morphed into their own "area":

Arrowhead / (northwest Phoenix & north Glendale)
Desert Ridge / (northeast Phoenix)
DC Ranch (among others) / (North Scottsdale)

One pretty common blanket way people describe the city is "Westside" vs "Eastside". It's not all that creative, but it comes with connotations. The westside has a more negative connotation for most as it's the grittier/poorer/more diverse/more crime area relatively speaking. The eastside is typically thought of as "better"/richer/etc. and lumps in all of the suburbs like Scottsdale/Chandler/Tempe/Mesa/Gilbert.