This feels a lot more like a Punisher story than Wolverine. Logan fights organized crime.
I suspect the reason it feels more like Punisher is because Frank Tieri was imitating the kind of gritty crime stories Garth Ennis was telling in Punisher.
It goes on for way too long, and you’ll see when we get to Wolverine #186 that Logan is even wearing a Punisher shirt on the cover.
So, yeah, Logan’s identity is being subsumed by Frank Castle.