So this was trickier than I thought.
I have a .sql dump of a database and when I imported it it was saved as wordpressblog.
I wanted it to be naylorfamily.
There is no rename function and so I needed to revert back to the command line and did it like this
mysql -u xxxxx -p"xxxxxx" wordpress -sNe 'show tables' | while read table; do mysql -u xxxxx -p"xxxxxx" -sNe "RENAME TABLE wordpress.$table TO naylorfamily.$table"; done