Absolutely not. Am American, so I’m gonna go on a limb and assume most of my friends would also probably pronounce it similarly.
The way you say Jra-gon and Dra-gon is completely different in most accents on the West coast. I’m very confident in that.
I think the Midwest would probably say it pretty samsies because they’re not emphasizing the first letter: jRa-gun / dRa-gun or jra-Gn / dra-Gn. Probably gets lost in the sauce a little.
Idk about East Coast, but tbh it probably is closer to Midwesterners dropping consonants and shit so who knows.