The idea was to create a compound index that was unique on name and user together. This way a user could create as many shapes as they wanted as long as each of their shapes had a distinct name. And the inverse was supposed to be true as well - shapes could have the same name as long as they had different users. It didn't work out like that for me.
What I noticed was that aside from the index on _id, three other index entries were created. One each for name, user, and name_user all set to be unique. I made a modification to the schema and included unique: false to each of the fields I was using for the compound index and suddenly it all worked as expected. What I ended up with was:
Looking at the indexes that were created as a result I still see the three indexes - name, user, and name_user. But the difference is that the first two are not set to be unique where the last one, the compound, is. Now my use case of multiple distinct shapes per user, or identically named shapes with different users works like a champ.