It has no specific name, it is the Spanish flag with the Spanish coat of arms with the Eagle of Saint John Evangelist. This coat of arms was first used by the Catholic Kings.
The coat of arms represents the union of the kingdoms of Castile (castle), León (lion), both on Isabella's side, with the kingdoms of Aragón (the red bars over yellow background) and Sicily (the two small eagles), on Ferdinand's side.
Though these were the kingdoms represented, the Catholic Kings ruled over many more kindoms, most of them in the Iberian Peninsula (Castile, León, Aragón, Toledo, Valencia, Galicia, Mallorca, Sevilla, Córdoba, Murcia, Los Algarves, Algeciras y Gibraltar, Barcelona, Biscay and Molina), and others abroad (Sicily, Sardinia, Corsica, Athens, Neopatria, Rousellon, Oran and Gociano).
Later the symbols of Granada (1492)
and Navarra (1512, after Isabella's death) were added, when the kingdoms became part of the Spanish Crown.
General Francisco Franco used during his rule (1939-1975) the same coat of arms with some changes:
The legend "Tanto Monta" was changed by "Una, Grande, Libre", and Heracles' pillars (with the legend Plvs Vltra) which had been added to the Spanish coat of arms long before were now represented with Saint John's Eagle.
The flag was later changed in 1977, two years after Franco's death to the following:
And in 1981 the eagle was removed.
Nowadays some Franquist followers use the following flag, which is just a modern/wrong version of the older ones, what is ignored by most people.
Aswell King Charles I of Spain, Emperor Charles V of the Holy-Roman Empire, used the following Habsburg coat of arms:
As you can see the Heracles' pillars were already there, but the two headed Imperial Eagle must not be taken for Saint John's.