Then about the only unifying name would be that of a river (the Avon), unless 'ghastly outer Perth sprawlburbia' counts (and I'm sure it doesn't).
Looking at the electoral map, Perth North works fine.
Not really.
It's all the nonmetropolitan shires from Gingin to Beverley and the "greater part" of the two northeastern intra-metro government units (the city of Swan and the shire of Mundaring to the south of it). So if anything it'd be Perth North
east... but really it's more an exurbanized rural (what Aussies call "regional", ie not the extra-remote bush country) district than anything describable as part of the city of Perth. And thus should not be named Perth.