The A205 is the ‘South Circular’ road, an ‘inner ring road’ through south London. So it is assigned that number by the highway authority (‘Transport for London’ in this case). But all the individual segments of it it will have street names (assigned by the borough councils).
The ‘A205’ designation is used on road signs to help motorists follow the route.
The street names are used to form the address for properties, for postal deliveries, legal things, etc.
Pretty much all roads in the UK follow this same logic.
I can recommend the Making sure you're not a bot! site as a treasure trove of geeky information about UK roads, including how they are classified.