On the relationship map, a label sits on top of a character's name. Can that be fixed?

Yes, from version 1.9.22. Each label on the relationship map (in the Codex, under Relations) is now placed along its own line where it covers no portrait, no character's name and no other label. On a very crowded map it takes the spot that covers least. This also applies to the picture you save with "Download PNG". Update BookyAI and open the map again: nothing else needs to be done.