Gwyneth

Gwenyth is not an alternate spelling of Gwyneth. The two have different sounds. Gwenyth is pronounced with the short "e" sound as in GWEN-ith, whereas Gwyneth is pronounced with the short "i" sound as in GWIN-eth.

I really think that this is a very beautiful name and I am glad to have it. But I think that it is high time people started pronouncing my name right! My name is not Gwen, it is Gwyneth. If you don't understand how to pronounce my name then just pretend that the y is making an i sound. Like win. Well, that is all for now!

I cannot stress this comment enough! It's also my name. Be aware that if you name your child Gwyneth, people will be mispronouncing and misspelling it their entire life. The correct, Welsh pronunciation is using an 'i' sound. If you want to name your child Gwen, maybe you could call them Gwendolyn. Even many of my long-time friends pronounce my name with an 'e' sound simply because they don't know better and it's more common.
To anyone considering naming their daughter Gwyneth:
Please carefully weigh and consider how important it is for your daughter to have an unusual/foreign name with how important it is that anyone spells or pronounces it correctly.
All I will say is that, nobody calling me by my real name, with an 'i' sound, gets old. It gets really old. It matters more than you might think.