You can use rnm. The command would be:
rnm -fo -dp -1 -ns '/pd0/.txt' -ss '\.txt$' /path/to/the/directory
-fo implies file only mode.
-dp directory depth. -1 makes it recursive to all subdirectories.
-ns implies name string i.e the new name of the file.
/pd0/ is the immediate parent directory of the file which is subject to rename operation.
-ss is a search string (regex). '\.txt$' regex searches for file with .txt at the end of the filename.
/path/to/the/directory this is the path where the v_1, v_2 ... directories reside. You can pass the directories ( v_1, v_2 ...) too in place of the parent directory path. For example:
#from inside the parent directory
rnm -fo -dp -1 -ns '/pd0/.txt' -ss '\.txt$' v_*