Currently the displayname and user_id for users is generated from a SAML response on user registration. How this is done exactly depends on which of the two algorithms you select in your homeserver config.

If someone wants to customise this, they'll have to fork Synapse, add in their own algorithm, and then try to upstream it, maintaining their own fork in the meantime.

This is not fun. instead, just like we do with password providers, we should allow Synapse to ingest third-party modules to provide the mapping functionality instead. This way everyone can use the same Synapse codebase, but customise their own separate module as they please.