>c) add new database fields to our customer tables for the names in each applicable case. Then we could reenter all the name data for all the men, and reprogram the application to support multiple names :-(
>(my czech contact swears that they only new two cases)
>
>Anyone have experience? How do you all Central Europeans manage this?

I'd go with (c). Then if there are applicable rules, apply them to the default value for the vocative case while entering names, but still leave it to the human operator to decide whether the rule applies or we have an exception. Then store whatever the operator says.