Strong Vow, and then Moon Shadow as in Moon's Shadow or Shadow of the Moon, then?
Vow(Promise) - vesta
Strong - thalion
Moon - Isil(sindarin)/Ithil(quenya)
Shadow - (sindarin) ath, dae, gwath, wath, weth (quenya) lumbule
Since quenya is the elven equivalent of our latin, as in it is the roots of the modern language, but used only in ceremony, names would largely be restricted to the modern I.E. sindarin.
So it would come out to
Vestathalion - Strong Vow
ves-tah-thahl-ee-on
Athisil (ah-thih-sihl), Daeisil (day-ih-sihl), Gwathisil (qwah-thih-sihl), Wathisil (wah-thih-sihl), Wethisil (Weh-thih-sihl) - Moon Shadow
So you would get Vestathalion for Strong Vow, and then you pick from any of the options for Moon Shadow for the surname. The names would be separated by a space, not apostrophes, as they are almost exclusively used in or following adverbs.
So you would have Vestathalion Daeisil if you were to choose the name closest to your original approximation.