For each file a_file in current directory rename a_file to lower case.

for a_file in *;do mv -v "$a_file" `echo "$a_file" | tr [:upper:] [:lower:]` ;done; 

¹⁾ For upper case reverse the arguments to [:lower:] [:upper:]

for a_file in *;do mv -v "$a_file" `echo "$a_file" | tr [:lower:] [:upper:]` ;done;