Why did he say "Hashem Adoneinu"?
Radak: You are Master of the created beings above and below.
Malbim: Shem Hashem is Chachmah and ability in which He is revealed through the existence that He created. This is why He is called Hashem. (His essence is hidden from us. The name that we call Him is based on what we recognize. It is called Havayah, for He makes endure and creates everything that is found.)
Why does he marvel at the majesty of Hashem's name?
Rashi: It is greater than the power of the lower beings. They were not worthy that You make Your Shechinah dwell among them!
Radak #1: This is like Mah Adir Atah. Hashem and His name are one. This refers to His four letter name (Havayah), which is not a To'ar (description). It is Adir (awesome) that You put Your Hod on Shamayim.
Radak #2: Your name is Adir in all the land, because You put power in upper beings to conduct the lower beings. Above conducts everything below - the land, sea and all that is in them.
Why did he say "b'Chol ha'Aretz"?
Radak: Your Gevurah is seen is the entire land - in settled areas, Midbar and the sea.
Malbim: The primary Chachmah and Gevurah via which we recognize Hashem's name through his creations, is only on the land and its offshoots. The Divine light that He shined on the creation it is on the land, and there is His latent power. Shamayim receives only light that returns from the land, like the moon receives from the sun.
What is "Hod"?
Radak: It is power and beauty.
Does David ask Hashem to put His Hod on Shamayim?!
Shabbos 88b: This was the angels' claim against giving Torah to man 1 .
Rashi: It is proper that You put it on Shamayim. In Your great humility, You make Your Shechinah dwell in the Mikdash.
Radak: Your great Hod and awesome power is seen in Shamayim. The land is small relative to Shamayim, like a point in a circle. "Tenah" is Makor (like an infinitive) in place of Nasata (You put). Makor can be used in place of past tense. "Yaldah v'Azov" (Yirmeyah 14:5) is like v'Azvah; there are similar examples. It can also be used in place of future or present tense. Also refer to 8:2:2:3.
Malbim: The Chachmah and ability seen in Your deeds on the land, they put Your Hod on Shamayim. The Torah testifies that Shamayim sends rain based on actions on the land 2 . The land influences, and Shamayim receives Hod. All the simple elements (earth, fire, wind and water) have simple laws 3 . How many Chachmos and inventions are found in composites 4 , which researchers have not discovered! All Chachmos of creation are in man 5 , and also intelligent speech, which ties the physical and spiritual worlds.
Lev Eliyahu (Shemos p.142): Why did the angels not want Torah to be given to man? Receivers of Torah rule over the entire creation. Via Torah, people could impose Shevu'os on angels! Hashem needed to change Shamayim to prevent this.
Malbim: Philosophers say that Shamayim is elevated above [concern for] the land and what is on it. They looked only at physicality. The sun is immensely greater than the earth, and its force pulls the earth and planets that orbit it; surely the earth is less important. They erred. The value of a skilled craftsman's work, e.g. a machine, is not due to the substance, rather, due to the Chachmah used to make it. An inventor is more esteemed if he gathered Chachmos into a small Kli (e.g. a clock the size of a lentil, with wondrous fine wheels inside).
Malbim: E.g. gravity applies to all physical substances. It fixes the trajectories of all the celestial bodies. Due to it, a stone thrown up will [later] fall to the ground. Air's nature is to spread. Via this, vapors rise, rain falls, and wind blows.
Malbim: E.g. vegetation is nourished; the food is converted to its nature. It regenerates like its blossoms, flowers and seeds to preserve its species. Living beings have even more Chachmos, e.g. sight, hearing and the other senses, and the Nefesh.
Malbim: Even though his body is weak - a newborn baby is helpless - there is awesome Chachmah in every limb.