Calling the invocant an object would be misleading though, as it's often just a string class name.

"Invocant" is being used as an English word, without necessarily the same meaning as in Latin. Consider how wildly the meaning of words like "genius" have been altered when borrowed into English. Altering the meaning is fine. I don't think many people are being confused by how the term differs from what they learnt in their Latin classes. The whole medical community is out there using words like "tonsillitis" (Latin word with a Greek suffix) and "dehydration" (Greek word with a Latin prefix and a Latin-derived suffix) and I don't think that the world perceives doctors as stupid as a result.