Nguyen (Vietnamese Nguyễn) is Vietnam’s most common family name, written with the Sino-Vietnamese character 阮. That character is also the Chinese surname Ruǎn (Cantonese Yuen)—so the US spelling is a romanization of a shared East Asian surname graph, not an English word.
What 阮 originally denoted is disputed in the sources: an ancient place/state name and an old plucked instrument (ruan) both appear in explanations. Separately, Vietnamese history repeatedly pushed people toward this surname during dynasty changes, which helps explain its huge share of the population. For a family card: it is a Vietnamese lineage name with Chinese-character roots; do not invent a cute English translation.