Phalacrocorax is a genus of fish-eating birds in the cormorant family Phalacrocoracidae, order Suliformes. Members of this genus are also known as the Old World cormorants.

Suliformes maybe from Old Norse Sula +‎ -iformes for boobies, gannets.
phalacrocorax (“coot, cormorant”), from Ancient Greek φαλακρός (phalakrós, “bald”) (from φαλός (phalós, “white”) + ἄκρον (ákron, “top”)) + κόραξ (kórax, “raven”).
"Cormorant" is a contraction derived either directly from Latin corvus marinus, "sea raven".
Carbo is from specific name Pelecanus carbo Linnaeus, 1758, Great Cormorant.

1/ Great cormorant (Cốc đế, Phalacrocorax carbo), known as the black shag
2/ Indian cormorant or Indian shag (Cốc đế nhỏ, Phalacrocorax fuscicollis)