Possible names would be:
Spanish/Hispanic Commonwealth (Mancomunidad Española/Hispánica), Spanish/Hispanic Crown (Corona Española/Hispánica) or Overseas Union (Unión de Ultramar).
As for it's division, likely one per viceroyalty, with members being New Spain, New Granada, Peru, La Plata, Spain proper and the East Indies, with other candidates being New Galicia, Chile, the Antilles, Aragon, Africa, Venezuela and California/New Mexico/Whatever lies to the north.