Did you know that if you subscribe to Azure AD Premium you also get licenses for FIM? Well if that isn't a hand tipper I don't know what is. I think we can safely assume the next version of FIM will have Azure in the name. Safe or not I am going speculate that it will.
Azure Identity Manager (AIM) -- I would be ok with this
Azure Role Based Access Manager (ARBAM) -- Explosive sounding name
Azure Provisioning Engine (APE) -- Please no!!
Azure Identity Technology (AIT) -- pronounced 8 or aight. Nah.
Azure Identity Sync Lifecycle Engine (AISLE) -- Certainly when people walk down the aisle they have an identity changing event.
Azure Identity Lifecycle Management Engine Next Technology (AILMENT). I really hope not we want to cure ailments not install one for you.
My Official guess -- Azure Identity Enhancements (AIE)
Unless we have already seen the new product name -- Azure Active Directory Premium (AADP).
Maybe the on-premise version will have a slightly different name
Azure Active Directory Premium On Premises Edition (AAD POPE)
The above has been pure speculation. I have no inside knowledge on the name.