I think
Magda is fine on its own (even though I personally prefer it as a NN
Magdalene, simply because I love the name
Magdalene so much that I'd rather have both of them instead of just
Magda on its own). Some nicknames sound too weak and informal on their own, but I don't think
Magda is one of them. It's a strong, warm name on its own, too.
Magda Cecilia sounds great. It's sophistocated, but down-to-earth.