[Answer]-How to do this search logic in django

You can see how to make a dynamic OR’d together query at How to dynamically compose an OR query filter in Django?.

Do you need to do it this way, though? Case-insensitive regex queries are quite slow.

Are you using PostgreSQL for your data store? If so, you could investigate the full-text indexing capabilities. That would give you a much faster way to perform these kinds of searchers.