לע"נ מרת אסתר בת ר' שמואל
The Minchas Chinuch [430] writes that מדאורייתא you don't have to mention Hashem's name in bentching. You can use your own words and be yotzei. The "Aderes" writes that this is a diffiult assertion to defend. The pasuk says black on white ואכלת ושבעת וברכת את ה' א-להיך!! "Eat etc. and bless Hashem your G-d" which means that his name must be mentioned. In the same vein Birkas Hatorah which is derived from the pasuk כי שם ה' אקרא הבו גודל לא-להינו also requires us to mention Hashem's name. So the פשוטו של מקרא tells us to use Hashem's name.
But then he tries to defend the Minchas Chinuch based on the Yerushalmi [Brachos 7/1] that learns a גזירה שוה from the word "שם" that it says regarding ברכת התורה. In order for it to be a valid גזירה שוה the word "שם" must be a מופנה - free and not needed לגופו. So if it is not needed לגופו that means that there is no requirement to mention שם השם.
