My grandfather was the one who immigrated here, though actually a son of his (an uncle of mine) came over first. My grandfather was originally recorded with the Hebrew name Benzion (In fact, this is my own Hebrew name, as I was named in his honor) though it was sometimes spelled Bencion (as in the naturalization certificate which my father showed me many years ago). The naturalization certificate includes an order changing his name from Bencion Gilenson to Benjamin Gilson. (The change from Gilenson to Gilson apparently began with my uncle, as he is recorded as Henry Gilson on military records from the US Army in WW1.)
One correction in my title. It appears that Druia is not in Latvia, but in Belarus today. However, there seem to be a number of Gilenso(h)ns who were born in Druia and recorded in Rezekne, Latvia (then Rezhitsa, Russia) in an 1897 census. My grandfather does not appear in the part of the census that JewishGen has online, at any rate; I don't know if JewishGen's list is incomplete or my grandfather was somehow missing -- or even that he may have been somewhere other than Rezekne in 1897.