Recently, a client wanted to rename whole bunch of existing teams in Microsoft Teams. They wanted to ensure the connected SharePoint team site names are updated too.
Renaming team in Microsoft Teams using 'Edit Team' setting won't change the connected SharePoint team site name! 😡
The best way to rename team in Microsoft and ensure the new name is reflected in SharePoint, you have to use the SharePoint Online Admin Portal and change the site name and URL (if required) from the active sites setting as shown in the image below.