When exactly would he had done so? Anakin was dubbed Vader maybe a day or two before Obi-Wan barbecued him in a lava pit, and he only learned of it just before leaving to do so. Not a lot of opportunities, let alone reason to address him by his formal Sith title, especially since as previously noted; Obi-Wan had yet to fully accept and process what Anakin had become. When he did, that's when he used the title, as we saw.
So yeah, this is not a thing that ever needed to be "justified".
I don't know where people get this idea that Jedi are adverse to ending people. Literally the first time we saw a lightsaber drawn in combat was Obi-Wan using lethal force to break up a bar fight of all things (at least that was the intent of the scene as written, whatever other storytellers may have retconned about their fates.)
Point being: Jedi aren't Batman. They have no compunctions about maiming or killing opponents if necessary. Indeed, literally disarming people is their signature move when threatened. They just do it dispassionately, and discriminately. Drawing a blaster on a Jedi is historically a very good way to loose a hand after all.
I also contest the claim that Vader was "crippled". This is a man that can crush your body into mulch with his brain. I don't care how many limbs you hack off the bugger he's still lethally dangerous.
Also; that's not the definition of an attack. That's ending a fight that the other started, which is exactly what Jedi are trained to do.