Using -mindepth 1 will ensure that the top directory is not selected.
$ find ./myfolder -mindepth 1 -type d
./myfolder/test2
./myfolder/test2/one
./myfolder/test2/two
./myfolder/test
./myfolder/test/a1
./myfolder/test/a1/a2
./myfolder/test/a1/a2/a3
But a -not -name test2 will not avoid subdirs inside test2:
$ find ./myfolder -mindepth 1 -type d -not -name 'test2'
./myfolder/test2/one
./myfolder/test2/two
./myfolder/test
./myfolder/test/a1
./myfolder/test/a1/a2
./myfolder/test/a1/a2/a3
To do that, you need something like prune:
$ find ./myfolder -mindepth 1 -name test2 -prune -o -type d -print
./myfolder/test
./myfolder/test/a1
./myfolder/test/a1/a2
./myfolder/test/a1/a2/a3
But do not use delete, as it implies depth and that will start erasing from the longest path:
$ find ./myfolder -depth -mindepth 1 -name test2 -prune -o -type d -print
./myfolder/test
./myfolder/test/a1
./myfolder/test/a1/a2
./myfolder/test/a1/a2/a3
Either use rm -rf (remove the echo if you want to actually erase):
$ find ./myfolder -mindepth 1 -name test2 -prune -o -type d -exec echo rm -rf '{}' \;
rm -rf ./myfolder/test
rm -rf ./myfolder/test/a1
rm -rf ./myfolder/test/a1/a2
rm -rf ./myfolder/test/a1/a2/a3
Or, also use maxdepth if all you need is to delete directories (and everything inside) (remove the echo to actually erase):
$ find ./myfolder -mindepth 1 -maxdepth 1 -type d -not -name test2 -exec echo rm -rf '{}' \;
rm -rf ./myfolder/test
A -delete will still fail if the directory is not empty:
$ find ./myfolder -mindepth 1 -maxdepth 1 -type d -not -name test2 -delete
find: cannot delete ‘./myfolder/test’: Directory not empty