I read the wiki on this but i Waze does not following it from what I can see Permalink
Do I change them to the most local name so in this case the city could be Doxford Park, Silkworth or even Moorside according https://www.ordnancesurvey.co.uk. Any feedback on how I tackle this would be much appreciated.
It’s a thorny question, and one for which there is no good answer, I’m afraid.
The best guidance I can give you is this post (particularly the second half) that I made a couple of years ago. Although it never did get written up in the Wiki, it seems to be the most acceptable advice around.
The main thing is not to get too detailed. These tiny locality names may be very meaningful to the people who live there, yet be completely meaningless to someone who lives on the other side of Sunderland.
It’s very difficult to find a good source of accurate boundaries, so don’t get too worried about giving every segment a city name.
Any segment may have several different valid names, depending on how closely you are focused, so anything you use will be invalid from some point of view. For example, I live in Bellingham; which is in Catford; which is in Lewisham; which is in London.
Also consider the area you are able to edit. If one corner of Sunderland “disappears” and is replaced by a cluster of small locality names, the “centre” of Sunderland on the Waze map will shift and the whole area will look lopsided. Unless you’re familiar with the whole city and able to do a fairly complete job, it may be worth leaving things as they are. 
I am happy to leave them, but the roads next to that dont have a city and did not feel it was right changing them to Sunderland or leaving it when editing for speed. My map shows the area as Silkworth so where is that info pulled from?
Agreed, still the most useful guidance, although I do think the situation in cities like Sunderland has changed since the introduction of Counties in Waze and the inclusion of Unitary Authorities like Sunderland in that list.
In the past, Sunderland would have been part of Tyne and Wear, but with Sunderland now considered the county it does give the possibility of splitting the city into named areas.
That’s not to say we should, just that we could :!:
Cardiff and Bristol are mapped this way - but as Iain says, you do need a consistent approach to the whole city so that you end up with a sensible list of suburbs and a centre.
Personally, I do like to see residential roads having a city name as it should help with street name searching; although Waze often seem to ignore this are display information from Google instead :roll:
What shows in that top corner of the screen is a bit variable. It’s influenced by what cities are around, where you have recently panned and other influences. For example, I opened your original UR and zoomed in to show the area in your last picture. WME said I was in Sunderland. I then zoomed out and panned a bit, looking for Silkworth. When I “returned” to the same area in WME, it now said Silkworth!
You can try enabling the Cities layer to get an idea of where city names have been applied - although there are a fair few overlaps here, so it may not help a lot. I notice that Doxford Park is “smeared” - there are some segments over by the eastern end of Doxford Park Way, then some right up against the A19. Timbones’ Colour Highlights script can also be helpful to find segments named with a particular city name.
The Doxford park area is a good one, if you consider the road Doxford parkway road, Morrisons Doxford park and not all of Doxford International Business Park are not in there either.
Considering that Sunderland only area, has East Herrington, Silksworth, Doxford Park and Farringdon around it seems that we should tidy that area up from just being Sunderland don’t you think?