One’s full Hebrew name is their first and middle names (if they have one), and their mother’s name. For example: David ben (the son of) Sarah, or Miriam bat (the daughter of) Rivkah.

The main reason for mentioning the mother and not the father of the ill person is the verse, “bring salvation to the son of Your maidservant,” which specifies the mother.

Another reason for specifying the mother is because we can be sure who the person’s mother is, whereas the father’s identity is never unquestionable. Obviously when praying for someone’s life, we do not want to confuse his/her identity through using mistaken lineage. Another related reason is that a Jew’s spiritual essence is inherited via his or her mother (whereas the father determines tribal association). When we pray for someone’s life, we want to emphasize their essential and eternal link to G-d, as derived from their mother’s side.

According to Jewish teachings, the primary physical features of a child come from the mother, whereas the main spiritual traits are from the father. This also explains why when praying for physical well-being, we mention someone’s mother [and when praying for soul, as in the case of a departed person, we pray mentioning the father’s name.]

In a case when the person’s mother’s name is entirely unknown, the person’s name should be appended with “…ben (or bat) Sarah,” referring to the matriarch Sarah, who is the mother of all Jewish people. If the mother’s non-Jewish name is known, however, it should be mentioned, as in “…ben (or bat) Elizabeth.”

In case of a convert, she or he should refer to themselves as the daughter or son of Sarah.