No. It is not necessary to have an engagement ring in order to be
engaged. If you choose not to have an engagement ring, you may want to exchange other engagement gifts or tokens. Some couples exchange earrings or necklaces; others exchange gifts that are not jewelry.
Some ideas:
Obviously, some of these gifts have more "lasting value" than others.
Some people think it's very important that an engagement gift be of
lasting value. Others don't find this important.