Seem pretty straightforward to me:
$ mkdir /tmp/sandbox
$ cd /tmp/sandbox
$ mkdir v_{1,2,3}
$ touch v_{1,2,3}/file.txt
$ rename -v 's#/file##' v_{1,2,3}/file.txt
rename v_1/file.txt v_1.txt
rename v_2/file.txt v_2.txt
rename v_3/file.txt v_3.txt
$ ls -F
v_1/ v_1.txt v_2/ v_2.txt v_3/ v_3.txt