What do we learn from "Tov Lehodos la'Shem"?
Radak (1, citing Shocher Tov): Adam was created on Erev Shabbos, sinned, was cursed, and was expelled from Gan Eden. Hashem came to give to him the verdict that he will die; Shabbos entered, and removed it 1 . Adam thanked Shabbos, and sang Shirah to it. Shabbos said, do you thank me?! I and you must thank Hashem - "Tov Lehodos la'Shem."
Radak: Shabbos is better to Hashem 2 than the other days, for man is free from his worldly engagements, and his Neshamah is clear from bodily distractions, and engages in Chachmah and Avodas Hashem.
Radak (91:1, citing Shocher Tov): This shows that Moshe said this corresponding to his Brachah of Yehudah, about whom it says "ha'Pa'am Odeh Es Hashem" (Bereishis 29:35).
Malbim: This refers to conduct via Hashgachah.
Why does it say "u'Lezamer l'Shimcha Elyon"?
Radak: The Neshamah Elyonah finds place to praise You, for You are Elyon.
Malbim: This refers to general conduct via nature. Shimcha ha'Elyon was publicized among the Goyim - they call him the G-d of gods, and He is Elyon (supreme) over all of them.