What is the central government of Spanish?

The central administration of the Spanish language is the Real Academia Española (Royal Spanish Academy). They are responsible for determining proper spelling conventions, whether a coined/new Word is acceptable Spanish, and publish the official dictionary of the Spanish language.

If you mean to ask what the central government of Spain is, that would be central government in Madrid, made up of the King, his royal entourage, the two houses of Parliament (the Senado and Congreso de los Diputados), and the Highest Courts of Spain (the Supreme Court and the Constitutional Court).