I believe in a great many things

How Dalish clans view and assign child-rearing doesn't in any way resemble the nuclear family. I’m extrapolating this from banter between Merrill and Sebastian:

Merrill: What does your Chantry do? Merrill: I mean, you keep saying how great it is. Anders and Isabela tell me to stay away from it. But what does it do? Merrill: Among the Dalish, the Keepers teach the children, preserve our history, perform magic. The priestesses here just... sing. Sebastian: The Chantry does many charitable works. It cares for widows and orphans— Merrill: Who in the Dalish would just be part of the clan, like everyone else. Merrill: I just don't get it.

So, from the time she was taken in, she’s had an extended support system which includes, but doesn’t revolve around, Alanari (and Sabina). It helps her form a stable sense of identity as she gets older, even if she doesn’t ever feel truly at ease with any religion (that’s another post altogether).