I've just started watching this show (first 3 episodes) and I'm wondering why he just doesn't have spare clothes stashed away somewhere from where he emerges from the water every time as it always seems to be from the same place?
Also, wouldn't someone/the police realize that the same guy keeps appearing in the nude from a swim in the river and think there may be something wrong with him?
I think the answers to both of those questions is that he doesn't die enough for 1) stashing clothes away to be needed/feasible and 2) he doesn't die enough for the cops to catch on.
If you think about most people can go 80+ years without dying no reason to think Henry would be any different. He does try to avoid death when he can. So I think his death in the subway in the premier was his first death in a while. If he's only dying every 40-50 years what's the point in hiding clothes? It's just when we pick up his life during the show he's in a more dangerous/adventurous time so he's dying a little more often.