I would call it "Mubaaraat Divorce" and then explain it or provide references. It is unlike any divorce in Civil/Common Law jurisdictions, so I would prefer to leave it as "mubaaraat" just in case.

https://ar.wikishia.net/view/طلاق_المباراة

https://almerja.com/fatawa/readPost.php?pid=551

The Mubaaraat differs from the khul’ in three things:
1- It results from the hatred of each spouse for the other companion, unlike khul’, which results from the wife’s hatred only.
[...]