I think it sounds really cool and heroic, but I agree that it definitely sounds like something an American otaku would call himself, rather than an actual name. I'd like to see it used on actual Japanese men.
Although it's a moderately popular name for boys (and a popular name to choose for a stereotypical Japanese boy), back in the olden days, Ryū was used as a girl's name. Based on some research that I've done (gathering names from passenger lists and US census data), Ryū was uncommon for girls in the late Edo period and the Meiji & Taishō periods.2 syllable names were preferred at the time, more so before the Meiji period, which is why Ryū was seen as a girl's name. Towards the 2nd half of the Meiji period and the Taishō period, those types of names were quickly shunted out in popularity by names ending in *ko.
With regards to the first line on my previous comment, I realised that I rushed it over a bit and only looked at the 2012 survey by Benesse (which you can see here http://tamahiyo.jp/namae/2012/).I didn't mean to say it is moderately popular. It is uncommon for baby boys but it (龍) did spike up popularity in 2012, which is the Year of the Dragon, then fell down back below the top 100 in 2013. Looking at data I've compiled from namaejiten.com, it saw a similar spike in 2000 and fall in 2001, below where it ended up in 1999. So, there is, still, a relationship between the year in which the zodiac symbol falls into and the number of babies being given kanji that represents the symbol (so long as if that kanji is either a Jōyō or Jinmeiyō kanji), like the kanji for dragon (龍). Considering this, I am expecting to see a spike in popularity again for 龍 in Japan in 2024. Fingers crossed.
This name is overused in Japanese video games to such a ridiculous extent that TV Tropes actually has a big list of characters named Ryuu or variations. Something tells me that Street Fighter is to blame. Honestly, I'm getting a little tired of hearing this name constantly. It sounds like something an otaku would call themselves, and I doubt it's really that popular on real Japanese men. People really are just using it for its meaning - why not try something with a little more life to it?
It just sounds like the ridiculous name of a fan character, usually coupled with other names. It's supposed to be simple and mysterious. I think it's overused for its meaning.
We native English speakers often pronounce this name "REE-oo" or "RIGH-oo," but neither is correct. Instead of separating the R and Y, try to pronounce them together: "ryoo."
Phoenix Flower is absolutely correct about the pronunciation. Many people don't know that, because they've never heard a Japanese person speak. They only hear the actors in the English dubs of animes, videogames, or wherever else you could possibly hear it.