The arrival of the long-awaited child marks the peak of a fulfilled divine promise, capturing the sheer wonder experienced by two elderly parents. The name given to the child is not a random choice made by a joyful father. Instead, it is a precise and immediate fulfillment of a command God gave before the child was even born, carried out on the very day of his birth [רד״ק, מלבי״ם]. Because God Himself established this name from the start, it remained entirely permanent. Unlike Abraham, Sarah, and later Jacob, whose names were altered or expanded over time, this child's name was never changed [אבן עזרא, מחוקקי יהודה].
The name itself embodies the miraculous, unnatural reality of a child born to a hundred-year-old father and a ninety-year-old mother. Such an impossible event naturally sparks deep wonder and laughter [רש ר הירש, אור החיים]. The shared joy of the parents is reflected in the dual acknowledgment of the child being born to the father and borne by the mother. This dual focus points directly to the laughter of both parents: Abraham, who laughed upon first hearing the news of an heir, and Sarah, who laughed within herself [ביאור יש״ר, ביאור שטיינזלץ]. Beyond capturing the emotions surrounding his birth, the name also holds subtle hints about the child's future essence and the path his life will eventually take [ביאור שטיינזלץ].
Emphasizing the mother's specific role also serves to highlight the child's unique status, clearly distinguishing him from Ishmael. He is the true heir, the only son suited to continue his father's legacy and fulfill his deepest hopes, a standing he holds precisely because he is the son of the righteous Sarah [אור החיים, מלבי״ם]. This reality reflects the power of the couple's mutual prayers. Abraham had prayed specifically for offspring from Sarah, and she had prayed for the exact same thing; the child's arrival proves that both of their prayers were answered [אור החיים]. From a different perspective, emphasizing Sarah's role served a vital public function. At the moment of naming, Abraham wanted to make a clear, public declaration to remove any lingering doubts among the masses, firmly establishing that this miraculous child was undeniably his own [העמק דבר].