It's An-wen and yes, it would not only be non-Welsh and incorrect to pin your own do-it-my-way pronunciation on it, it would be disrespectful and intolerant to do so. It's a foreign tongue with it's own alphabet, pronunciation and proud tradition, no Burger King. If you like Anven, make it up and spell what you mean.
To get a V sound in Welsh you need to spell it with a F. Anfen. And no, it isn't a name. You can make up Anven in modern American/Australian/Canadian English if you like but it will have no connection to Welsh at all and thus no meaning.