That's how they are traditionally pronounced.
Morrigan's an old Irish name. Names like
Eoghan (sounds like
Owen) or
Oonagh (sounds like OO-na) are other examples of silent G's.
Personally, I've never heard of
Aylin, but according to a few comments, the Turkish pronunciation is indeed eye-lin.
I kinda like
Morrigan pronounced both ways, but traditionally it'd be the first way. If you wanted to say it like MOR-i-gan, then I'd just consider it a different, trendier name.