The name does not matter, the whole point to it is that the sentence can be taken 2 ways, that the mans name is Smith (which is what most will think) and that the wooden leg is named Smith (which is the joke part). The joke is a 2 person joke, one person can not tell it alone and both have to be in on it really, the first part is the starter, who says they know a person with a wooden leg named Smith, the bystanders assume that the mans name is Smith, then the second person responds with something like "Really? What's his other leg named?" making it seem as if they assumed that Smith is the legs name. It's the misunderstanding and the odd picture it creates in your imagination (well everyone elses since you don't seem to have a good one really) that makes it funny. Either way it's more of a joke for someone who can think more simply and not over analyze things (which you are doing), if you think too much you will ruin it for yourself, it's funny cause who would name their wooden leg anyway? It's a kids joke meant to be understood by kids and those who know not to over think.
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