Why is Great Britain called Great, and not just Britain?

Some say it was King James who first called Britain "Great Britain" when he styled himself the first King of Great Britain in 1603.

However, the name was first used 1,500 years before that.

Where does the Great, in Great Britain, come from?

Claudius Ptolemy wrote a book sometime between AD 100 and AD 170, called the "The Almagest", where he referred to 'megale Bretannia' and 'mikra Brettania' as the islands currently known as 'Britain' (England, Scotland and Wales) and 'Ireland'.

The word megale in Greek meant great or huge.
The word mikra in Greek meant small or little.

"Britain" comes from the Latin word: Britannia or Brittania.  Greek may have been Bretannia.

The original spelling of the term, Britannia, Brittania and Bretannia is disputed. But they are all close enough to be deemed as the modern word 'Britain'.

So, we have:

megale Bretannia meaning Great Britain.
mikra Brettania meaning Little Britain.

Hence, Great Britain is the Big island in the British Isles.