The name 'East Anglia' isn't derived directly from the Anglia Peninsula itself (which as you say is located in what is now known as Schlesweg-Holstein), it's derived from the people who lived on the Anglia Peninsula (the 'Angles') and who subsequently migrated and settled in England after the Romans left. The land in which this settlement in England took place was called 'Anglia', from which the name 'England' itself is derived, and covered a wide area of the country. East Anglia was so named as it was the easternmost part of this settlement.

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Below is a link to a map showing this settlement as at 600AD (taken from William Sheppard's 'Historical Atlas' from 1923, similar maps can be found on wikipedia but it seems they are all derived from this one). As can be seen, similar settlements by the Angles further inland were referred to as 'Middle Angles' and 'South Angles'. Coincidentally, it also shows how the names of the two counties that currently make up East Anglia (Norfolk and Suffolk) also received their names, they were the 'North Folk' and 'South Folk' of the East Anglia settlement.

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https://legacy.lib.utexas.edu/maps/historical/shepherd/britain_settlement_600_1923.jpg

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