Growing up in South London, even after privatisation, I always remember how heart stoppingly exciting I thought “Network SouthEast” sounded and looked
I've always thought that Network South East sounded dynamic, Network North West though didn't sound as dynamic as NSE did but it did appeal to me as the northern version of it. All we had in Yorkshire was either MetroTrain (focusing on West Yorkshire), Network South Yorkshire (which sounded more of a Tesco Value version of NSE) and in North Yorkshire and the-then Humberside, Regional Railways.
Network South East use to have the "flash" on the entrance totem poles (as did Network North West), yet Regional Railways didn't and I think that they should have as it would have sold the brand a bit better.
When Northern are on strike you do often hear the Guard Manager often state that its a MetroTrain service to... in West Yorkshire or a Network South Yorkshire service to... in South Yorkshire but I've never heard it being announced as a Regional Railways or Provincial service to... outside of South or West Yorkshire. I'd imagine that for the north west that Network North West would be used.