In short, no.

The word "Soviet" is from a Russian word for advice, council o.s. Russian being a Slavic language this derives from the proto-Slavic vět-iti ("to inform"). Through shared indo-european roots it is thus related to English "wise", (which is the root in "ad-vis-or"), Dutch weten ("to know"), Norwegian "viten ("knowledge") etc.

The name Việt Nam is a variation of Nam Viet (南越, Nányuè; lit. "Southern Việt"), where the word Việt originated from Bach Viet, a group of people then living in southern China and Vietnam, and the form "Vietnam" (越南) is first recorded in the 16th-century. Vietnamese being an austroasiatic language, it shares no known roots with the indoeuropean language group where the Slavic languages belong.

There is none.

The Russian word "совет" (sovet, "council") derives from the Old Slavic word "вече" (veche, also "council") while the Vietnamese "Viet" as far as I know comes from the name of a people that inhabited the region Vietnam is located in today.