I have exactly the same problem, unable to rename Slingplayers since the push update sent last week. Under settings, the "Edit" button to rename the Slingbox does not work.
Called Sling support and they advised that function does not work through browser version of viewer and need to install Desctop Slingplayer. Installed, but still unable to edit Slingplayer names.
Hope Slingbox support is monitoring this community thread...