See the pedant in me wouldn't want to see it named the Enfield Line as it goes to two different destinations, calling it a destination as the name of the line would indicate to first time users that all trains go to Enfield. For example if you are on an Enfield Line train that doesn't go to...
They don't really have their own names currently, just their technical route names. North London Line, East London Line, West London Line, Gospel Oak to Barking Line, Upminster to Romford Line, Watford DC Lines and Lea Valley Lines.
No they aren't although they are more traditional. Think its a good idea to split them up in some form, as they do have different frequencies/share routes, but I don't think I'll be calling it anything more than their old names.
Its not the worst idea to rename them, I imagine people will be angry about it for some reason because Sadiq Khan came up with it or something. I don't actually think the names are THAT helpful, they should have been renamed as the Overground as having all one colour is confusing to some, but I...