You can rename Trints and Stories from within the file itself by clicking on Edit next to its current title.
You can also do this from the My Trints and Stories list:
Go to My Trints and Stories list
Click on the checkbox next to the Trint, Story or Caption file
Click on the Rename button in the top toolbar
Note, you will not be able to click on Rename if you have multiple files selected.
You cannot rename files in the Shared With Me list.
If you would like to duplicate a file from the Recent Trints list, please find it in your My Trints and Stories list and duplicate from there.