Cathryn

That would depend on whether there was a formal introduction right away. If they first encountered each other, like, mid-fight-against-bad-thing, it would take longer. But you know that as soon as Jack got a clear look at John, he would be pulling out the flirty smile all, "Captain Jack Harkness. I don't think I caught your name."

And John would just be like, ". . . Winchester," because a fellow hunter flirting with him is really the last thing he needs on a hunt, so Jack would naturally turn up the charm a notch, which is probably the fastest way to get on John's nerves, but if this is post-fight here (presumably post-unsuccessful-fight or there wouldn't be much of a story) then he's already seen what Jack can do. So he'll suck it up as best he can for the time being because it's clear that this thing is too much for one hunter and the hunt comes first.