Suppose my brother is named Bob, my father is named Robert, and my mother is named Roberta. Do these three people all have the same name? This is obviously not a question about their birth certificates but about the permissible usages of the expression "the same name."
I understand there is a narrow usage of this expression which would require exact match of orthography. But is there also a wider usage that counts the names as the same? It's clear what etymological connection these expressions have to each other; they share an etymological lineage. But do people ever use the term "one name" to pick out these lineages? Would you ever say these names are the same, or would you always resist that and insist on saying they only descend from the same name?