I will use an example from Swedish. This example does not hold universally for Swedish, and I doubt anyone who has it even has it in every register (i.e. at least in one commonly known prayer, there is an exception).
For some speakers, in most contexts, far and fader ('father') are exchangeable, as are mor and moder. There is, however, an exception: for some, fader and moder cannot be used as a vocative. (Possibly with the sole exception 'fader vår ...', which is part of the Lord's Prayer.)
Now, consider a language in which such pairs are common. Would 'antivocative' or 'avocative' be a good term for the synonym that is restricted from occurring as a vocative?
Could similar names be used for forms that cannot be used as complements or maybe as subjects or as objects be a reasonable term? "Antinominative", "antiaccusative", "anticomplemental", etc?
This type of thing is probably not entirely uncommon in the languages of the world, but as a phenomenon it's a bit underreported or underdescribed.