El Shaddai means 'God Almighty'...a nice name for a deity but a bit much to live up to for a mortal girl child ;o)
Shaddai is the plural of Shad from the word shaddad meaning 'to be strong or powerful'. In the Hebrew of the Bible Shaddai occurs no less than 48 times and in every single case refers to God himself and is rendered 'almighty' in translation. Assuming a bit of Christian faith on the part of anyone listening to Amy Grant, if it were me I'd probably neutralise the cheek of applying El Shaddai to a child by dropping the El bit (which means 'God') and working with Shaddad - Shadda maybe, 'to be strong'. But then I personally wouldn't name my child Jehovah, Elohim or Yahweh either. Or name them a foreign term the meaning of which I didn't know or understand because it was in a pretty song come to think of it ;o)
Devon