How do we understand "Hashem will not abandon His nation due to His great name"?
Rashi: He put His name on you, that He is your Savior, and lest His name be diminished.
Radak: It became known among the nations that Hashem desired You to be a special nation for Him. If He would not bear you, and punish you according to your sins and destroy you, it would be as if His name was diminished among the nations, and they would say 'He cannot save them.' And so Moshe said "the nations who heard about You will say, because Hashem cannot?" (Bamidbar 14:15-16), and Yehoshua said "what will You do to Your great name?!" (Yehoshua 7:9).
Malbim: This refers to verse 20, "do not fear?" If you will serve Him, you need not worry lest His desire for you will change. This is impossible - (a) Due to His great name - He is known to be your protector. [If He ceased, the nations] would say 'because Hashem cannot?' (b) Hashem began to make you a nation. His will does not change!
What is the meaning of "Ho'il Hashem"?
Rashi: He swore. This is like "va'Yo'el Sha'ul Es ha'Am" (14:25).
Malbim: He began.
