In Shmuel Aleph, when Shmuel becomes a Navi, he runs to Eli each time Hashem comes to him thinking it is Eli not Hashem. After the fourth time Eli realizes it is Hashem and tells Shmuel (in paraphrase) that the next time he is called to say "Hashem your servant is listening". When it actually happens that Hashem calls Shmuel leaves out the word Hashem and just says "your servant in listening".
Many commentaries give the reason why this is so, but I am not interested in that as much as, aside from the book of Esther, are there any other places in Tanach where Hashem's name is missing?