I speak Dutch so obviously I'm biased as I know how to pronounce it. But I don't think it's a big issue. If it was, say, Evelyn, people would need to know whether she was an Ev-lyn or an Eve-lyn for example. Most people only need to be told once.
It's not exactly 'een' though, it's a slightly different sound misses point of thread
I would anglicise it too to Evelyn to prevent a lifetime of mispronunciation.
I have an Eve, simple and straightforward I thought but she is always being called Evie (ev-eee) as this is the more 'common' name. I dread to think how people would cope with Evelien although I understand it is Dutch etc. It even annoys my daughter now she is older think of your daughter!