You have a point, but wasn't the UK referred to as 'Great Britain' or 'the British Empire' or just 'Britain' during that time, not 'the United Kingdom'? Through that lens, just using the name 'Spain' makes sense.

Answering the second question:

Portugal and Spain had the same king, but the Crown was separate. Kingdom of Spain and Kingdom of Portugal.

Internal matters were handled by Portuguese officials, the Portuguese Inquisition was independent from the Spanish one.

All in all, a certain degree of independence was maintained. (This was only during the reign of Filipe II of Spain, I of Portugal, the following kings changed it, which contributed to the rise in dislike of Spain and the subsequent war and revolution in 1640)

Matters pertaining to the Portuguese Empire were handled in Spain though, which led to the start of the fall of the Portuguese Empire.