Currently, Teamwork does not have the ability to give custom terminology at the initiative level since Initiatives are not a record type, nor innately visible, in Teamwork. However, when attempting to create a custom lookup/relation field OR creating a relationship to a linked record, the related workspaces terminology does not carry through on the field name. Ex: the related workspace with a team's initiative is "Campaigns", but when relating to a campaign in Teamwork it displays only as "Initiative".
Language confusion across various teams and workspaces when relating and viewing work details
Allow for each team to have a custom terminology for Initiatives even though they cannot be created or viewed within Teamwork.
If the above is not possible, create dynamic functionality so that if a custom field were to be created on an activity in Teamwork to lookup related workspace Initiatives then the field name displays appropriate to that workspace's terminology. Same for related tab with linked records.