Its all in the subject line. Is there some physical limitation that disallows files to be renamed on SD cards?
Read-only tab activated (ignored by an Arduino though), but otherwise no.
Maybe since the included SD library doesn't implement a rename function (for some reason), it doesn't mean an Arduino can't do it. In fact, SdFat (https://github.com/greiman/SdFat) can and it runs in most of the "Arduino boards".