A typical PTv2 route would consist of one route master relation, with the individual routes (e.g. an one for eastbound, one for westbound trips) as members (without a role). 
If any of the trips took an alternative path, these would be added as separate routes within the same route master also.
In this particular case, we had one route master (relation 15594524) that contained another route master (relation 15594510), which then contained the routes. Hence, the "real" route master was "nested" within another (redundant) route master, which I removed. 

Regarding the names, the PTv2 scheme does explicitly define how the name tag should be used. For bus route masters that is "Bus<ref>"  and for bus routes it is "Bus <ref>: <from> => <to>". When multiple bus routes would end up getting the same name this way, "Bus <ref>: <from> => <via> => <to>" should be used.
The official_name tag is a good place for the descriptive name.

You can find more detail about the naming here: https://wiki.openstreetmap.org/wiki/Buses

The original proposal that PTv2 is based on is here (it defines the naming conventions in this exact way also): https://wiki.openstreetmap.org/w/index.php?oldid=625726