add my mother's last name to my name

when my husband and I got married and added my married name. No hyphen or anything, just another name to add to my line of relationships. Then when I was pregnant, we talked about “losing” a family name which neither of us wanted to happen. So my son took on several new names: his first, his grandfather’s first, my family name (which is my mom’s), and my husband’s last name. Alot of names, but mostly just for history and family lineage.