MySQL has a RENAME TABLE statemnt that will allow you to change the name of a table.
The manual mentions
The rename operation is done atomically, which means that no other session can access any of the tables while the rename is running
The manual does not (to my knowedge) state how this renaming is accomplished. Is an entire copy of the table created, given a new name, and then the old table deleted? Or does MySQL do some magic behind the scenes to quickly rename the table?
In other words, does the size of the table have an effect on how long the RENAME table statement will take to run. Are there other things that might cause the renaming of a block to significantly block?