Baning is an Anglo-Saxon masculine name composed of ban (bone) and -ing (one possessed of the quality of), thus meaning: possessed with the quality of bone.
Baning [Henry Harrison 1907-1918 Surnames of the United Kingdom 1: 20].
Bænincg [Sir Allen Mawer, Sir Frank Stenton, & Sir Frederick Houghton 1927 English Place-Name Society 4: 196].
Bæning [Hugh Smith 1964 English Place-Name Society 39: 60].
Ban = Bᴏɴᴇ [William Smith 1873 A Complete Etymology of the English Language, page 84].
-ing = a suffix forming derivative masculine substantives, with the sense of ‘one belonging to’ or ‘of the kind of’, hence ‘one possessed of the quality of’ [Sir James Murray 1901 A New English Dictionary on Historical Principles, 1st edition, 5 (I, J, K): 282].
The place-name Baeningesburg, mentioned in a charter issued by Uhtræd of Hwicce [John Kemble 1839 Codex Diplomaticus Aevi Saxonici 1: 179], is believed to contain Bæning [Hugh Smith 1964 English Place-Name Society 39: 60].