Why did David compose this Mizmor?
Radak: These six Mizmorim until the end of the Sefer are all praises of Hashem. Therefore he began with Tehilah and ended with Tehilah; also this Mizmor begins with Tehilah and ends with Tehilah. The other five begin with Hallelukah and end with Hallelukah. When will Hashem's praise be great? When the exiles are gathered, the entire nation will see wonders that Hashem will do with Yisrael. Therefore it mentioned the gathering of exiles and the building of Yerushalayim. One who contemplates it will see the wonders of the Creator and His judgments with His creations 1 .
Seforno: David prays that he be able to make many return to Avodas Hashem, and that Yisrael will merit this in the future.
Radak: Therefore, Chazal said (Brachos 4b) that anyone who says this Mizmor three times a day is guaranteed to be a Ben Olam ha'Ba. This is not just for saying it with his mouth, rather, with his mouth, heart and tongue.
How will he aggrandize Hashem?
Radak: With his heart and tongue. You are the true king; all the kings and leaders, above and below, are under Your authority, and you are elevated above them.
Why does it begin with Aromimcha (elevating Hashem Himself), and end with "Shimcha" (His name)?
Radak: This teaches that He is His name, and His name is Him. This refers to His name that is written, but not pronounced; the other names are To'ar (descriptions).
Malbim: Hashem Himself is hidden; He is revealed via His actions. He is elevated above understanding. You Yourself are exalted above all Brachos and praise. However, I bless Your name - what You were publicized via Your conduct. Brachah of Hashem is the influence and good that comes from Him to our world via virtue of lower beings. You are the source of Brachah and good. Hashem is like a king hidden in his honor, elevated above all his officers and servants, and still Brachah comes from him to his entire nation. Via this, His name is known and blessed.
What is "l'Olam va'Ed"?
Radak #1: His name.
Radak #2: I will bless You forever, i.e. my entire life.
Radak #3: I will aggrandize You in this world, and bless Your name in the world to come, which is l'Olam va'Ed.
