Currently, origins in the archive are identified by their IRI, such as this one: https://archive.softwareheritage.org/browse/origin/https://gitorious.org/systemy-zdarzeniowe%C4%85%C5%9B%C4%87/systemy-zdarzeniowe-gitorious-wiki.git/directory/
However, database schemas (origin-related tables and skipped_content), variables (grep -Ri url swh-environment/*/swh), APIs (origin-related tables and skipped_content for swh-storage, all origin arguments of swh-web), specifications, and documentation refer to them as URLs.
IMO, the easiest solution would be to keep the current format and names, and just update the specifications/documentation to mention they are actually IRIs