How Are Hebrew Names Formatted?

"How are Hebrew names formatted?

Also, given that Hebrew names customarily identify a person as either the son or daughter of their parents, what are some options for individuals who do not use gendered designations?"

The customary format for the Hebrew name of a Jewish male is [First name] ben [Jewish parent’s name] v’[other Jewish parent’s name], for example David ben Yosef v’Chanah or David son of Joseph and Hannah.

For Jewish females, the format is the same: [First name] bat [Jewish parent’s name] v’[other Jewish parent’s name], for example Leah bat Moshe v’Rachel.

Individuals who become Jewish through conversion choose (or in the case of a child, are given) a Hebrew name upon their conversion and are known as the child of Abraham and Sarah, the biblical figures regarded as the spiritual ancestors of every Jewish person.  

People who choose not to use gendered designations might substitute mibeit (from the house of) or mimishpachat (from the family of) in place of either ben (son) or bat (daughter). Such a person’s Hebrew name might be, for example, Rivka mibeit Leah v’Rachel or Rivka from the house of Leah and Rachel.