"It is Yahweh your God and no one else whom you will honor; it is he alone whom you will worship, and it is by his name and only his name that you will swear." Your language may have another way of emphasizing that Yahweh is telling the Israelites not to worship or serve any other god.
To swear by the name of Yahweh means to make Yahweh the basis or the power on which the oath is made. The metonym "his name" refers to Yahweh himself. 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/jit/figs-metonymy]])