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General Information:
Moses speaks to the Israelites as if they were one man, so all instances of "you" and "your" are singular. (See: rc://en/ta/man/translate/figs-you)
him will you worship
"he is the one you must worship"
To him you must cling
To have a good relationship with Yahweh and to completely rely on him is spoken of as if the person were clinging to Yahweh. Alternate translation: "You must rely on him" or "He is the one you must rely on" (See: rc://en/ta/man/translate/figs-metaphor)
by his name will you swear
To swear by the name of Yahweh means to make Yahweh the basis or the power on which the oath is made. Here "name" represents Yahweh himself. See how you translated a similar phrase in Deuteronomy 6:13. Alternate translation: "you will swear and ask Yahweh to confirm it" or "when you swear you will speak his name" (See: rc://en/ta/man/translate/figs-metonymy)