The SD.MonitorMigratedIncidents project is responsible for creating the entries in PM. I would check that project. It's probably just a matter of changing the Setup Process component a bit for Process Name/Process Description.
It's also possible to mark up IncidentMigrator to add/append more fields. You should be able to extend the migrated incident type in SD.Data if you need to. Once IncidentMigrator is modified, The IncidentMigrationWizard needs to be updated with the new Migrator resource (IncidentMigrator is a resource used by IncidentMigrationWizard)
And I would test, test, test any changes