What is the meaning of "l'Shem'a Ozen Yisham'u Li"?
Rashi: Even not in front of me, they will obey what I command through messengers.
Radak: L'Shem'a Ozen is like "va'Ya'as David Shem" (8:13) 1 . Yisham'u is gathering, like "va'Yshama Sha'ul Es ha'Am" (Shmuel I, 15:4), because people gather via hearing announcements.
Malbim: [Nochrim far away, who initially denied me,] will now hear and gather to me even without seeing my power - just due to hearing the wonders done for me.
Radak (8:13): He became famous for winning a major war.
Why will they lie to me?
Rashi: It is amidst fear of me. Radak - they will deny that they fought against me.
Radak: They will deny (loyalty) to their Ba'alei Bris for me, like Aram, which had a Bris with Amon, and when they saw that they were stricken, it says "v'Yashlimu Es Yisrael va'Ya'avdum va'Yir'u Aram Lehoshi'a Es Bnei Amnon" (Shmuel II, 10:19).
Malbim: Nochrim far away initially denied that there is Am Yisrael and their king David.