The right long-run solution is to refactor Bahmni such that the local name is stored in OpenMRS as a PersonName (rather than PersonAttributes). However this sounds like a significant amount of work, and might require introducing something new to OpenMRS, like a “Name Type”.
I do think that having multi-word searches work better against person attributes would be generally useful, but we’d want to ensure it doesn’t adversely affect performance in a notable way.
Actually, in recent Bahmni releases we’ve upgraded to use a version of the OpenMRS Platform that indexes patients in Lucene for faster/better patient searches. But we have not fully refactored Bahmni to take advantage of this. So maybe the most efficient solution is to see if PatientSearchBuilder can be refactored to use the Lucene API instead of the SQL generation in PatientAttributeQueryHelper.