Every template card has a context menu (the … button) with Rename, Duplicate, Move, and Delete. To act on several templates at once, select them first and use the action bar that appears, which covers Move, Duplicate, and Delete.
Rename
Open the template's … menu, choose Rename, and type a new name.
Duplicate
Duplicate creates a copy in the same folder, with " copy" added to its name. Select several templates to duplicate them all at once.
Move
Move opens a folder picker. Choose the destination folder, and the template (or every selected template) moves there.
Delete
Delete removes a template permanently.
A template that is currently used by a campaign cannot be deleted. Its menu shows Delete (used by campaigns) greyed out, and a bulk delete tells you which of the selected templates are affected. To delete one of these, first remove it from the campaign, or delete the campaign entirely, then delete the template.