Gillingham means a "homestead of Gylla's family", from Old English ham "village, homestead" and ingas "family, followers". First recorded in 10th century as Gyllingeham
Godmersham seems to recall Godmærs village, from the Old English ham village, homestead. It was first recorded in 822 as Godmeresham.
Goodnestone denotes Godwines farmstead, from the Old English tun farmstead, village. There are two in Kent, the one near Faversham first appearing on record in 1208, and its namesake near Aylesham a little earlier, in 1196.
Gores name is a little more pedestrian than it seems, indicating literally a place at the triangular plot of ground, from the Old English gara. It first appears on record in 1198.
Goudhurst is probably an eponym, indicating Guthas wooded hill. The final element is the Old English hyrst wooded hill, and the place is first seen on record in the eleventh century as Guithyrste.
Grain is first seen on record in about 1100 as Grean. The name represents the Old English greon, used for gravelly, sandy ground. The Isle of Grain, which was once a true island, first appears in 1610 as the Ile of Greane.
Grange is a realtively common place-name in England which tends to go back to the Middle English grange farm belonging to a religious house. Kents Grange, however, is clearly different: its first recorded spelling in about 1100 is Grenic. This suggests that it is etymologically the same word as Greenwich, indicating a green harbour, from the Old English grene and wic port, harbour.
Old English ea indicated a stream or river, and it forms the last element of Graveney. Here it is combined with grafa ditch, pit, indicating a settlement at a ditch-stream. It is first mentioned in the ninth century as Grafonaea.
Gravesend has nothing to do with graves. Its first element is the Old English graf, the modern grove, and the town is thus etymologically a place at the end of the grove. Its first mention was in the Domesday Book, in the form of Gravesham, but we already see Grauessend by 1157.
Greatstone-on-sea is a recent name taken from a shoreline feature, since eroded by coastal changes, known as the Great Stone (first recorded in 1801).
Greenhithe is an Old English hythe or landing-place, and the adjective green can be traced back to its ancestor grene, as seen in the towns first recorded spelling of Grenethe in 1264.
Groombridge takes its name from Old English grome, which originally meant simply a young man. The town is thus literally a bridge where young men congregate, and it is first recorded in 1239 as Gromenebregge.
Guston is an eponym, in this case describing an Old English tun village, farmstead. It is first seen on record as Gocistone in the Domesday Book, and the sense is of Guthsiges village.