Why call the force the Commonwealth fleet rather than simply the English fleet?
Short answerBecause it served the developing Commonwealth union of England and Scotland, represented by the period flag shown in the presentation.
NotesA question about the English and Scottish flags leads into the term Commonwealth fleet. The displayed flag represents the regime's combined political identity rather than a later British Empire. The 1654 union measures formally joined England and Scotland within the Commonwealth. The terminology matters because the fleet was becoming an instrument of a wider state created by the civil wars rather than a continuation of an English crown navy under another name.