To clarify, the conversation was in English, the person I was speaking with gave no hint of knowing any language other than English. The confusion came because I was giving an (approximately) Mexican pronunciation of the name while otherwise speaking perfectly straight US English. The humor I found in the situation was nothing to do with the nice young woman who couldn't understand me, it came from two things. First, that even when I realized that the first time I'd said it I'd given it a more Spanish pronunciation and confused her and so I was deliberately trying, the second time, to pronounce it in the way that a non-Spanish-speaking English-speaker would, I still 'messed up' and said it the wrong/right way. And second, that I am still at so low a level of Spanish that it seems ridiculous that I should have a problem like this. That is the kind of problem I would expect to have if I were fluent, or somewhere close, instead of stumbling through "Two years ago, I was working at the airport. Where were you working two years ago?" stilted exercises from the first book.
I was, in other words, laughing at myself.
I hope that makes more sense than my original post? I wrote it the way I did to try to preserve some of the humor of the incident, but apparently in doing so I made things confusing.