If you are petitioning for divorce on the basis of your spouse's adultery, you don't have to name the third party.  If you do name them, they have to be served with their own set of divorce papers.  That potentially makes it harder for you to proceed with your divorce because you need not only the respondent but also the co-respondent to complete an acknowledgement of service form and return it to the court.  It's generally better not to name the third party.  Apart from anything else, it's usually interpreted as confrontational, which in turn can make it harder to reach agreement on the children or the financial arrangements.