Yes, COGNOMINA is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, G 2, N 1, O 1, M 3, I 1, N 1, A 1.

Is it a valid word?

COGNOMINA is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a familiar name for a person (often a shortened version of a person's given name)
the name used to identify the members of a family (as distinguished from each member's given name)

Also: family name, last name.