a name: the word a person, place, or thing is called by, which in the Bible stands for who that person really is and how they endure in the world.
In the Bible a name is rarely just a label attached from outside. It represents the person, their character, their standing among others, and their claim to be remembered. That is why a single Hebrew word stretches across things English keeps apart:
- the actual name you are called
- the reputation that name comes to mean
- the revealed name of God
- the authority someone acts under
- the name that lives on after you die
These are one idea seen from different angles, rooted in a common ancient Near Eastern understanding that a name is the publicly available index of a person's identity and continuance. To give a name is to say what someone is or will be, which is why the naming scenes in Genesis so often carry an explanation, and why God changes a person's name to mark a turn in their life. Because the name stands for the person, acting "in someone's name" means acting with their full authority behind you, and a good or ruined name becomes the standing by which others know and treat them.
The same logic, lifted to God, makes his name the nearest thing the Bible has to his presence and character: to call on it, trust it, praise it, or profane it is to deal with God himself. The Deuteronomic language of God choosing a place to put his name there draws on the ancient Near Eastern royal convention of a conqueror inscribing his name on a monument at a site to claim it, so the formula asserts YHWH's sovereign ownership of the sanctuary rather than his absence from it.
And if your name is really you, then keeping it alive after death, through children or a permanent monument, is keeping you alive. The levirate obligation, the childless widow's petition, Absalom's pillar, and Isaiah's promise to eunuchs all turn on the same terror: to have no one carry your name forward is to be obliterated.