The terms concerning the Team and Channel elements highlighted in this picture are defined below.

 Renaming Team and Channels

1. The user to which the phone number is assigned may change the Team Name in the MS Teams application. 

Since it's the user making the change, it is not necessary for Global Admin to do a "Sync SMS App"

Note: The SMS Messages exchanged with a contact in Outlook or Microsoft Office 365 will appear in a channel following the name of the contact. If the channel is renamed, the channel name will be replaced in favor of the Outlook contact name when a new message arrives. 

2. Enterprise Admin may also change the Team Name to a desired alias. 

Search for the phone number, SMS user or Group name from the "SMS DID Management" screen and then change the "Current Team Name in Teams",

To propagate the Team Name change to user/s, go to Dashboard and hit the "Sync SMS App" button.

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.  

If 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.
 

1. Look for the deleted SMS phone number, Channels, or Team, then check the box, click Restore Group at the 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 appear in Teams again. Note that the restoration may take 4 to 24 hours, as we have to allow time for it to propagate. 

Restored SMS phone numbers, Channels or Teams 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.