I highly doubt that they translated directly from Hebrew. The first complete translation of the bible is the [明治元訳聖書]{めいじげんやくせいしょ}, which was first published 1880. It contained already the name エデン. Before this, attempts were made to translate a Chinese versions into Japanese.
In Chinese the modern name for Eden is [伊甸]{yīdiàn}. An older name (~1875) was [埃田]{āitián}, as can be found here on the left page the 9th column from right. But the āitián is modern pinyin and I don't have any experience in Chinese language history. But I guess the pronunciation was more like エデン. In Korean for example, the pronuncation for 埃 is still 애 (~= え). And 田 is even in modern Japanese でん.
So my unsophisticated answer would be: エデン comes from 埃田 which had a similar Chinese pronunciation at that time and because people prefered to translate from Chinese instead from Hebrew/Greek original texts.