"conversation" term confusion
You should coordinate with Office 365 Groups team with your naming convention. We started heavily rolling out Teams and O365 groups within organization and many users are confused how "conversation" within O365 group is not matching "Conversation" in teams. They think it is the very same thing. Here is my proposal:
They should either be the same. PROS: In such a case everything be in the same place you can continue, additionally if someone outside of group sends email to O365 group email it will be displayed in conversation in teams (reduces need to read emails). CONS: If you have large team it could clutter your group mailbox or personal mailbox if sending all copies.
Separate naming convention "Group mailbox" and "Conversation". PROS: Reduces confusion to users which conversation is stored where. CONS: It is creating additional place for end user to look for information (if not sending copy to inbox)