'Angus' and 'Valkyrie' both contain elements derived from the same root as the modern English choose.
Valkyries are female figures in Norse Mythology who hover over battlefields and gather up the souls the slain. carrying them to Valhalla, where they will spend their time alternately feasting and preparing themselves to fight in the last battle, Ragnarök, at which the gods will be defeated and the cosmic order overturned.
Valkyrie literally means 'slain chooser'. The first element valr is an Old Norse word referring to those slain in battle, and the second from Old Norse kyrja, 'chooser', which derives from a PIE root *gues-, whose meaning was 'choose' or 'taste'. It has a host of cognates in different languages, such as Spanish gusto, French goût, English disgust and choose, and Old Irish gus, 'strength', 'excellence', 'choice'.
And that brings us to Angus. The first element here is an-, from the same PIE root as English an, a, one. And you have probably already spotted the second element is gus, 'choice'. So Angus is 'one choice' or 'one excellence'.
It's interesting, and something I didn't know, that the word valkyrie survived into middle English but with meaning of 'sorceress'; the Middle English Compendium records the phrase "Wychez and walkyries' from around 1400.