The greatness of God's name in the world is permanently bound to His leadership over the Israelites and the eternal survival of the royal dynasty. The primary approach among commentators is that when God fulfills His promises, His name is elevated for all time. The entire world recognizes that He rules over Israel eternally and never breaks His word.
A deeper understanding of this dynamic reveals a striking parallel between the laws of nature and divine providence [מלבי״ם]. God guides the world through two parallel channels. The first is the natural order, which operates through fixed laws and the heavenly bodies. The second is miraculous and providential guidance, which responds directly to the actions of the Israelites. It is through this direct, miraculous involvement that God is revealed and recognized as the Master of the universe.
Just as the sun serves as the main instrument of the natural order, the House of David serves as the main instrument of divine providence. Because the physical elements of the natural world were created to endure forever, the instruments of divine providence, namely the Israelites and the royal dynasty of David, must also be eternal.
Ultimately, God's name will be exalted forever because all people will acknowledge and declare Him to be the eternal God of Israel [מצודת דוד]. He rules over the Israelites [ביאור שטיינזלץ], guiding them with a special, direct providence according to His will [מלבי״ם]. Within this divine plan, the dynasty of David will continue to exist [ביאור שטיינזלץ] and stand firmly forever without any change [מצודת דוד], as they are the chosen leaders meant to carry out this unique divine guidance [מלבי״ם].