Can't rename a file the name of which starts with a hyphen

Most GNU/Linux commands allow a -- option to indicate end of options so that subsequent - prefixed words are not treated as options.

  mv -- -example-file-name example-file-name

A small test

$ touch -- -example
$ ls -l -- *ample
-rw-r--r-- 1 rgb rgb 0 Nov 25 09:57 -example
$ mv -- -example example
$

RedGrittyBrick's answer is very good. Another option is:

mv ./-example-file-name example-file-name

A small test:

$ touch ./-example
$ ls -l ./*ample
-rw-r--r-- 1 me me 0 Nov 25 16:02 ./-example
$ mv ./-example example
$ ls -l ./*ample
-rw-r--r-- 1 me me 0 Nov 25 16:02 ./example