[Two years later, August 2018] You can do this now. In the sidebar to the left where the folders are listed, click on "More" and then on the "Create New Folder" option on the pop-up menu. Your new folder will appear at the bottom of the sidebar under "Recents" and you can catch it with your mouse and move it wherever you want to.
That pop-up menu will also give you access to the entire list of your existing folders (you first have to click on that option to see them). Once it's showing, you can click the folders you want to drop into the sidebar. To remove a folder from the sidebar, click on it and you'll get a drop-down menu with various choices including that one.
There still doesn't seem to be a function for re-naming folders (at least I couldn't find one) but - if you have a web-based account such as gmail/yahoo/hotmail/aol - you could try logging into it via your browser and making the change online. I haven't done this though, so it's just an idea for a possible workaround.
PS: I should probably mention that I'm using Spark on a laptop (MacBook, Sierra) not a mobile device.