All you've got to do is put as many identical lines in the data source as there are labels on a page. Personally, I would use MS-Access, and then an inner join between the data table and a table with the exact number of records in it (contents don't matter). You get a socalled 'cartesian product' and that's exactly what you want in this special case (most of the time cartesian products in a relational system are an error).
Doing it in Excel takes a little bit more work, although it can easily be automated in a macro: repeat (copy the data, paste after the end) enough times, then sort on the identification.
Hope this helps.
Is there any way to use the mail merge to create one whole sheet of mailing labels PER NAME?