I think it sounds pretty, also it reminds me of the cosmonaut dog "Laika" because they sound similar, but since I like both names it does not make me like it any less, overall it is a pretty name.
The meaning of "Taika" is inconceivable. I am an illusionist and conjuror (or magician, if you wish), so the essence (definition) strikes a chord. The name itself, as far as written spelling and to-the-ear pronunciation-- is less than astonishing, unfortunately. It holds a sense of "kre8tiv" (made up), especially in the United States, and near immature manner. It is a lovely name, nonetheless.
Judging by the official statistics it would seem that Taika has become more popular only in the 90's. It's not a common name but to my Finnish ears it definitely sounds like a name.
In my opinion this name is very unique, but a bit strange, too. One girl in my school bears this name and it fits for her very well, because she is a creative and unique person.
I've never heard of anyone with this name, and I don't remember reading or hearing that peole have started to use this. I find it impossible to imagine this name on a person. It would sound just as weird as Magic would in English usage.