Is this not possible in the browser version? I can't seem to see anywhere where I can select a file and attempt to rename that file....

There are several ways you can rename files on www.drivehq.com.

From the Show Folder page, which displays a list of files / sub-folders in the folder; if it is displayed as "Show Icons", then you can move your mouse onto the file name, you can then click on the file name and edit the file name;

If the folder is displayed as "Show Details", then you can find a column "Action". Move your mouse onto the action icon, it should popup a menu, which includes "Rename" function.