The terms are defined below with reference to the Team and Channel elements highlighted in this picture.
Renaming Team and Channels
The user to which the phone number is assigned may change the Team Name in the MS Teams application.
Since it is the user making the change, it is not necessary for Global Admin to do a "Sync SMS App" in this workflow.
Note: The SMS Messages exchanged with a contact in Outlook Contacts or Microsoft Azure Active Directory (i.e, organization contacts) will appear in a channel following the name of the contact. If the channel is renamed, it will be overridden in favor of the found Outlook or Azure AD Contact when a new message arrives. 
Restoring Deleted Teams and Channels
It is not recommended to delete a Team dedicated to an SMS phone number and any channels dedicated to SMS conversation with contacts.
In the event a team or channel has been deleted as illustrated above, follow the steps described here.
From the Microsoft Entra admin center (formerly Azure), navigate to Groups then Deleted Groups.
Look for the deleted SMS phone number, Channels or Team then check the box and click Restore Group on top of the page and click Yes on the confirmation message.
A notification will pop up on the upper right and the SMS phone number, Channels or Team should show in Teams again. Note that it may take 4 to 24 hours for the restoration as we have to allow time for it to propagate. 
Restored SMS phone numbers, Channels or Team will show at the bottom of the Teams Channel lists. 
If you create a Channel or Teams that already exists an error message will occur saying: “Channel name already existed, please use other names."
The workaround is to restore the channel from the Microsoft Entra admin center deleted Teams list.