This is the scenario:
MySQL statement-based replication (basic replication) works by running the exact same statements that were run on the master on the slave. This includes information about what database the table was in.
I don't think MySQL provides any built-in way to move replication statements between databases (i.e. "insert into db1.table1 ..." -> "insert into db2.table1"). You may be able to trick it by manually altering the replication logs on the fly, but it wouldn't be out-of-the-bod MySQL replication.