OK, so “burg” and its variants are common suffixes in Germanic place names, but what about “ham?”
Apparently, “ham” is an old Teutonic word meaning (roughly) “crooked.” This ultimately gives the cut of meat its name, but this question is not about meat.
Is there something about Hamburg’s topography that gives it that name? Or is it something else?
‘Ham’ is one way to spell ‘home’ in old Germanic (‘heim’ in modern German).
‘Burg’ refers to a fortified place.
Hence Hamburg should be seen as meaning ‘the fortified home’. Google it by searching on ‘Hamburg’, ‘etymology’ ‘ham’ and ‘burg’ this gives you a variety of cites. There is unfortunately no definite German dictionary online as long as Duden remain in the 20th century.