PASE lists 7 people by this name, including the king:
http://www.pase.ac.uk/jsp/pdb?dosp=VIEW_RECORDS&st=PERSON_NAME&value=10527&level=1&lbl=Anna
Foerstermann lists Anna as a continental Germanic name, noting an Anglo-Saxon form Anna as well. He does this in the section for the prototheme An- which he speculates is from Old High German *ano* "ancestor" and/or *an* "favour, grace". This is on page 99 of my edition.
(There's also Old English *an* meaning "one", but I'm not sure it was used as a name element.)
Presumably Anna would be a short form/diminutive for a longer dithematic name with the first element being An-. The ending -a is an Old English diminutive suffix.