When using phpMyadmin to backup a MySQL database, there is an option near the bottom to save as a file. When you use this option, you can make your life easier by using a file name template that automatically names the backup file for you. By default it is the database name, but I find it useful to put a timestamp on it as well. To do that, use the following in the file name template field:
%Y%m%d%H%M%S-__DB__
This will save your files in the following format: 20070815152612-databasename.sql