Nguyen is also a simplified version.
The real name is written with accent : Ngue^~n (both accents on the e). That's why, it's impossible to pronounce it right in English.
I tried once to teach the correct way to my friends and nobody can repeat it correctly, not even close, so New-yen is generally accepted...
Most of the time, Vietnameses will just say it's fine if it sounds anything close to it, they know that it's not possible to get it right.