Wise not to put faith in websites offering 'family crests'. I have to say that I've never encountered this name as English, only American.
I was dubious about the Kentish, even English, origin, but the information here -http://www.roots-boots.net/ft/l-eastes.txt
looks reliable. Note that the English spelling is Eastes, a name new to me, and very rare if it exists at all in England today. It could be a variant of Eustace, or from the word 'east'. Personally I'm very sceptical about the D'Este origin.