Yes, you can create categories/folders to organize your Templated material. To do so, open up the Templates library. In the upper right hand corner, click the folder + icon.
Name the folder as you'd like and select whether you want to save the folder to your Personal Templates or to a Team (Please note, only Team Leaders are able to create Template folders and Templates for Teams). Then, click "Create."
Once the folder has been created, you can edit the folder name or delete the folder by clicking into the folder in question and selecting either the pencil (edit) or the trash can (delete) next to the name of the folder.