My favorite name for a fraternal association is The Independent Order of Odd Fellows (IOOF). The Odd Fellows purchase cemetery plots so you will often see many deceased members of this association buried near each other. Their primary symbol is three chain links joined together. In the picture above the number 30 is the lodge number.
Sometimes the chain links will encircle the letters F, L and T like in the example below. These stand for friendship, love and truth.
Top photo: Fairmount Cemetery, Denver, Colorado
Bottom photo: Littleton Cemetery, Littleton, Colorado