You cannot rename a DB table without it being a breaking change. Therefore in a migration situation the existing tables would remain as they cannot be removed. In order to remove the table(s) all references would need to be dropped, the table renamed and then all the references added back. Given that this can be cascading it would be very expensive.
The only supported way, that I'm aware of, to rename a table is to use the sp_rename sproc. However if you read the docs on this it is strongly recommended that you do not use this as it won't fix up the references. The recommendation is to create the new table, update the references and then drop the old table.