As usual:
- Grid: TR 22260 65641
- Code: CT3 4EF
- WGS84: 51°20'47"N, 001°11'25"E or 51.34637,1.19016
JW: I checked Doomesday and Hasted and there were no references to Boyden apart from a couple of people mentioned in the latter. It's not mentioned either in the Kent Hundred Rolls of 1274-5. The Kent pubs website,
http://www.dover-kent.com/2014-project/Gate-Inn-Marshside.html, hazards a guess that the gate pub is named for it's proximity to the gate of the Arch Bishop of Canterbury's Hunting lodge at Ford.
One thing that Hasted does mention however is under the Rivers section. Talking about the Chislet area he says:
These waters, especially the Nethergong, are at most times narrow inconsiderable streams, being continually crossed by wears, gates, &c. set up as well by the commissioners of sewers, as private persons, for the convenience of the levels, though in the time of floods they are both frequently increased to a great width, and run with vast force and rapidity into the sea.
so it's just possible that the gate as in the place and the pub is named for a nearby sluice. Looking at the map the place seems to be a maze of drains and streams so this is (I hope) not too far fetched.