What does Long mean?
From Chinese (and Vietnamese) 龙 / 龍 (long, Mandarin tone lóng) 'dragon', a benevolent, imperial, rain-bringing figure. Note: it is a romanization of a tonal syllable, also spelled Lung in Wade-Giles/Cantonese; the same Pinyin 'Long' can represent the unrelated 隆 'prosperous, abundant', so the dragon sense is specific to 龙/龍.
What does Peng mean?
Peng is commonly the character 鹏, the giant mythical bird of Chinese legend.