Wouldnīt then be logical to rename them? AFAIK, user functions for a
    mode FOO are usually FOO-func1, FOO-func2, not FOO-mode-func1,
    FOO-mode-func2. I donīt think changing them would cause trouble, as
    users are probably using them throug bindings in occur-mode and not
    directly with M-x.

Yes, that renaming is ok if you want to do it.