Kay

“The significance of God’s name El Shaddai is both interesting and touching.
God (El) signifies the Strong One. The qualifying word Shaddai is formed from the Hebrew word ‘shad’ the breast, invariably used in Scripture for a woman’s breast; e.g. Gen 49:25; Job 3:12;Psa. 22:9; Song 1:13 (and more); Isa. 28:9;; Ezk. 16:7.
Shaddai therefore means primarily ‘the breasted.’ God is Shaddai because He is the Nourisher, the Strength-giver, and so, in a secondary sense, the Satisfier, who strengthened and nourished from the mother’s breast, but also is quieted, rested, satisfied, so El Shaddai is that name of God which sets Him forth as the Strength giver and Satisfier of His people.”
-1909 Schofield Bible

Trying to define ‘roles’ for God is rather like nailing Jello to the wall…