tar: --exclude=".git": Cannot stat: No such file or directory

All the options need to be together before the arguments, and the -f flag needs to precede the tar file:

tar -zcv --exclude='.git' --exclude='.gitignore' -f $NAME-$VERSION.tar.gz $NAME-$VERSION

This gives you what you want:

tar czvf $NAME-$VERSION.tar.gz $NAME-$VERSION --wildcards --exclude=.git --exclude=.gitignore