The document created by the Labels dialog contains a table, which is what you've been typing in. Just like any other table in Word, when you press the Tab key at the end of the last cell of the last row, you'll get a new row. In this case, it will put
the new row on the second page. At the end of that row, press Tab to get another new row, and so on.
If you need to manage that many names, though, you're probably better off using a mail merge. See
http://www.gmayor.com/convert_labels_into_mail_merge.htm and
http://www.gmayor.com/merge_labels_with_word_2007.htm.