standard error of what? the proportion of people who's cat name is (x) ?

My thinking:

If your trouble is that there are infinite categories, you can make it finite by having "other" as a category, along with other categories of your choice.

If you want to work out how many people you need to ask to have a good chance of picking up every name in use... this cant be determined (other than by judgment) without making assumptions about what the distribution of names is.