Schemas can be renamed by using the following code-snippet and replacing OLD with the old name of the schema and NEW with the new name of the schema and then executing it the struct-section of the administrative menu of the sqlite plugin.

UPDATE schemas SET tbl = 'NEW' WHERE tbl = 'OLD';
UPDATE schema_assignments SET tbl = 'NEW' WHERE tbl = 'OLD';
UPDATE schema_assignments_patterns SET tbl = 'NEW' WHERE tbl = 'OLD';
ALTER TABLE 'data_OLD' RENAME TO 'data_NEW';
ALTER TABLE 'multi_OLD' RENAME TO 'multi_NEW';

Please be aware that you still have to manually update all your aggregations.