The few times I've been asked it, mentioning it by name results in them swiftly moving on ... the one time it didn't, the person didn't recognise the name and insisted I'd provided the wrong answer - which was a huge time saver for me in terms of turning them down.
It's entirely possible they were trying to force me to defend the position I'd taken. It probably annoyed them that I took their pet interview question (that they expected me to struggle with) and shot it down in front of them. Not that I'm claiming any special skills - probability is a hobby of mine, this problem was a gateway drug into it and I work at the very low/noddy end of quantitative finance - so a certain familiarity with things like these is to be expected. I was more surprised the guy didn't recognise the name when I said it.
I'd go as far as saying that this question makes your interviewing process to be more "cheat-friendly" - the chances of an interviewee not knowing of the problem and solving it on the spot are a lot lower than those of him having heard of it and pretending to solve it on the spot.
The first time I heard of it I was surprised about how counter-intuitive it seemed, but it didn't baffle me completely because I have a strong information theory background. From an information-theoretical point of view, it's not completely counter-intuitive that new information can change probabilities a posteriori, particularly when there is mutual interdependence.
To be fair most explanations of the Monty Hall problem gloss over the most important fact, that Hall knows the correct answer. When I first learned about it I had a hard time comprehending it until I very carefully reread the description and realized this key fact.
I can't remember where I read it (or I'd provide a link) but the real "a-ha" moment for me came when I read "... so what if there's a million doors instead of 3? Does that make a difference" (it doesn't to the argument but it does to most people if you frame it in that way allegedly) in an explanation.
