What’s in a name? A variety of names have been used to refer to the country and language of interest here. The word Britannia is a Latin form which refers to the country where the Pritani lived and is derived from Greek Brettanoi which is what Ptolemy called the inhabitants of the island. Anglia is also a Latin reference to the land of the English.
The main name is, of course, English (Old English englisc) which refers to the language of the Germanic tribe from the area of Angeln in present-day Schleswig-Holstein. The word originally had an /e/ as first sound which was an umlauted form of the /a/ of the tribe’s name, the Angeln (Old English Engle). The second term is Saxon which derives from the Saxons, again a Germanic tribe from the North Sea area which came to Britain as of the 5th century AD; the label Saxon fell into disuse fairly quickly.
The study of historical forms of English has had various names throughout its history. The modern labels are simply Old, Middle and Early Modern English. But in the last century when Old English studies began it was common to call the language of the earliest period Anglo-Saxon. One finds this occasionally nowadays, e.g. in later editions of earlier books on the subject, such as those by Henry Sweet or William Bright.