As we continue with the opening supplication - دعاء الاستفتاح - we go on to say the phrase وتبارك اسمك which is commonly translated as, "And blessed be Your Name." But the word ‘blessed’ does not convey the same exaggerated, hyperbolic meaning as تبارك, for the word form actually indicates a completeness in the greatness and breadth of the blessing.
So when we then attribute this word to the Name of Allah, اسمك - Your name - we are acknowledging that Allah Himself is the source of all blessings, and that we are able to benefit from those blessings by using His name. Thus, when we begin our meal with the name of Allah, the devil is unable to share it with us due to its blessings. And when we slaughter an animal while invoking Allah’s name, it becomes pure and lawful for us to eat.
So when we say وتبارك اسمك what we are essentially saying is, “Your Name is so complete, magnified, and sanctified, and its blessings span the heavens and the earth, and invoking it is a cause of blessings to descend upon everything over which it is invoked.”