Here's how to change the names of your collections:
1) In My Collections, click on the Collection to enter Collection View that will show all the Moments within that Collection.
2) Click the "Editing Off" toggle button at the top right:
3) This will toggle to "Editing On" and give you options to change the name of the Collection or delete the Collection:
4) If you change the name of the Collection int he Collection Name box ("Parenthood" in the example above), it will automatically save and you can click the "Editing On" toggle to turn editing off.