linux - Recursive rename files and folders

I need to rename every subfolder of a specified path.
For example I have a directory structure like this:

project/
   /x
      /something
          /somethingElse
              /x
          /x.someext
   /notXButTheresXInASubfolder
          /something
              /x

and I need to change it to:

project/
   /y
      /something
          /somethingElse
              /y
          /y.someext
   /thisContainsXIntheNameButIsNotx
          /something
              /y

I would do this ideally with a bash script, but I have no idea on how to do it...

Answer

DIRS=$(find /path/to/project -type d -name "x" | sort -r)
while read R; do
  test -z "$R" && continue;
  B=$(dirname "$R")
  mv "$R" "$B/y"
done < <(echo -en "$DIRS")