Thanks for your answer and the interesting links!
site says the origin is Old English or Old German
They are not a name site but a site about saints. However they are usually reliable. Lots of names which have a German
orgin include the element "burg". That might have led them to believe that Cyneburg(a) could partly be Old German
. I guess "burg" was used by Old English speakers as well and Cyneburg(a) is 100 percent Old Englsih.