To add a new Folder you need to be an Admin user:
Select Settings > Studio > Picklist Settings > Edit Templates Picklist
On the next screen, select the Edit option on the Folders row
Add the options (one option per line) and hit Save to commit your changes.
Now when you are creating new Templates or editing existing Templates you can add them to the folder you have just created by selecting them under the Folders drop-down
Please note that the New Folder you have just created will not appear in the Template Selection Pop Up until you have saved at least one Template within it.