One of the (few) downsides of phpMyAdmin (at least the version I use) is that it doesn't support the mySQL rename table function.
It is very simple to use this function through the SQL tab in phpMyAdmin (or any other direct interface with mysql). Say you want to change the name of the table from "tbl_oldtable" to "tbl_newtable" then this would be the code:
RENAME TABLE tbl_oldtable TO tbl_newtable
Simple huh! Right with that duty to my readers and hopefully my natural search traffic... (these mySQL posts tend to do pretty well) I am off to drink more cabernet sauvignon :)