I usually give the old college try myself, as most of the time I will either get it right (and impress), or close enough to get a warm smile and friendly correction.
And the rare times I get it badly wrong, it's usually a good laugh had by everyone which doesn't bother me either.
On the other hand, if you know your pronunciation skills are shit -- or if you're not socially quick enough to smooth over rough patches in conversations, your best bet is probably just to ask them.
Either way, I certainly wouldn't put too much effort into learning cultural pronunciations and such -- like memph said, anybody who is that uptight about the pronunciation of their last name by a stranger from another culture probably isn't really worth getting to know anyway IMO.