In QM 1.2.14, to not show completed quests in the quest journal UI, your options are:
Untick the player's Quest Journal > Remember Completed Quests, or
Add a Canvas Group to the Completed Quest Name Template and set its alpha to zero, or
Make a subclass that overrides AddQuestToUI() to only add the quest to the UI if it's active.
In 1.2.15, Unity UI Quest Journal UI has a new 'Show Completed Quests' checkbox that you can untick to omit completed quests from the UI. If you're using QM 1.2.14 or earlier, you can download a patch here:
