It just because so many trendy names have the -on - an or -en at the end of the name turned to -yn, just to spice up a name (regardless of the inconvenience it is to have a name you need to constantly spell out). I think that's where these reactions came from :)
If you like
Haven, then maybe just use
Haven? I doubt she'll have anyone in the class with the same name as it was on place #433 back in 2012. And of course you've got the luxery of asking her for her opinion. Maybe she likes Haven/Havyn, maybe she doesn't. I think it'd personally try to find a name that isn't too far off of her birth name if I had to rename a 6 year old.
Good luck to you with the adoption and the decisions regarding her name.