Hi LC, I am not sure that there are actual bylaws/constitution for the Society of the Holy Name as everything refers to it being a spiritual society for Catholic men with roots that go back to the 1200s. If you go to the following site, though it has obligations, rules, how to become members, etc.
www.nomensanctum.org/Web%20Pages/Membership/membership_home.htm
I hope this helps but if it does not give you what you are looking for, let me know and I will keep searching. Take care and God Bless. P