Ri + u has no meaning in Japanese. Ri + yū means reason. Ryū means dragon, or it can mean flow, but usually as part of a compound word. Ryū as in the name of a character in the video game "Street Fighter" is a slightly unusual name. It is more common to see it combined with other kanji to form longer names (eg. Ryūichi Sakamoto).
Any of those can be first names, meaning the city hall will probably let you register any of those as a name. But the only one that is commonly used as a first name would be Ryū, but as I said, it is slightly unusual to see it on its own.
Japanese is a very unforgiving language, and slight variations in pronunciation can result in big differences in meaning. And, I suppose I don't need to emphasize this, but the kanji or hiragana (or katakana) spelling is what you need to be looking at. The English spelling is an imperfect by-product of the original Japanese intention.
Romaji/Hiragana/Katakana only provides the pronunciation, as Majestic-san mentioned. The meaning is determined by the kanji, so your question "what is the meaning of this word written in romaji?" is meaningless in most cases.