Tafsir of Al-Muzzammil 73:8

(And remember the name of your Lord) means: Continue to remember Him, the Exalted, night and day, in whatever manner that may be—whether through glorification (tasbih), declaring His oneness (tahlil), praising Him (tahmid), prayer, Quran recitation, or otherwise. The command is interpreted as an imperative for continuity, because he—upon him be peace and blessings—was never unmindful of Him, the Exalted, such that he would need to be commanded to remember Him, the Glorified. The intended meaning is continuity by custom, not literal continuity, as the latter is impossible. Furthermore, the requirement of the context is that this is a generalization following a specification; thus, the meaning is based on what you have heard regarding the consideration of night and day.

(And devote yourself to Him with complete devotion) means: Sever your attachment to everything other than Him, the Exalted, through worship. Strip yourself of preoccupation with anything besides Him, the Almighty, and be fully immersed in contemplating Him, the Glorified. This is a command regarding the inward state, following the command regarding the outward state. To emphasize this, He, the Exalted, said "a complete devotion" (tabtilan), and it is in the accusative case due to the verb "devote yourself" (tabattal) containing the meaning of "sever" (batala), as has been stated. A discussion regarding the verification of this has already preceded at the saying of the Exalted, "And Allah has caused you to grow from the earth a [progressive] growth," so reflect upon it, for there is no antiquity in the covenant, and regardless of how the matter stands, it preserves the rhythm of the verses.