MySQL multi-source replication with identical DB names
I briefly searched MySQL Documentation
I located the Rewrite DB Option embedded in a new mechanism : CHANGE REPLICATION FILTER
It allows you to manipulate the Rewrite DB stuff without restarting MySQL.
UPDATE 2014-04-02 15:48 EDT
After reading the MySQL 5.7 Docs, I can safely say that CHANGE MASTER TO and CHANGE REPLICATION FILTER still cannot help you. Here is why:

All databases are identically named on all Masters
Replication Filters are global in scope. It would be very convenient if a filter could be scoped toward each MASTER_BIND interface name. At this point, MySQL 5.7 does not do that.

ALTERNATIVE
Perhaps you should set up multiple MySQL Instances on the Slave Server. Make each MySQL Instance use standard MySQL Replication. You can scale down all the buffer sizes and settings for all the Instances on the Slave.
Then, you can set up a mysqldump from each of the MySQL Instances to different folders.
If you want to learn how to setup multiple MySQL Instances on a single server, please see my old posts

Sep 30, 2011 : Running multiple instances on the same host
Sep 17, 2012 : mysqlservice command syntax